Math formulas
There are three environments that put LaTeX in math mode:
math 	For formulas that appear right in the text.
displaymath 	For formulas that appear on their own line.
equation 	The same as the displaymath environment except that it adds an equation number in the right margin.
The math environment can be used in both paragraph and LR mode, but the displaymath and equation environments can be used only in paragraph mode. The math and displaymath environments are used so often that they have the following short forms:

\(...\)   instead of   \begin{math}...\end{math}
\[...\]   instead of   \begin{displaymath}...\end{displaymath}

In fact, the math environment is so common that it has an even shorter form:

$ ... $   instead of   \(...\)

The \boldmath command changes math letters and symbols to be in a bold font. It is used outside of math mode. Conversely, the \unboldmath command changes math glyphs to be in a normal font; it too is used outside of math mode.
The \displaystyle declaration forces the size and style of the formula to be that of displaymath, e.g., with limits above and below summations. For example:

$\displaystyle \sum_{n=0}^\infty x_n $

Subscripts & superscripts
In math mode, use the caret character ^ to make the exp appear as a superscript, ie. type ^{exp}. Similarly, in math mode, underscore _{exp} makes a subscript out of exp.
In this example the 0 and 1 appear as subscripts while the 2 is a superscript.

\( (x_0+x_1)^2 \)

To have more than one character in exp use curly braces as in e^{-2x}.
LaTeX handles superscripts on superscripts, and all of that stuff, in the natural way, so expressions such as e^{x^2} and x_{a_0} will look right. It also does the right thing when something has both a subscript and a superscript. In this example the 0 appears at the bottom of the integral sign while the 10 appears at the top.

\int_0^{10} x^2 \,dx

You can put a superscript or subscript before a symbol with a construct such as {}_t K^2 in math mode (the initial {} prevents the prefixed subscript from being attached to any prior symbols in the expression).
Outside of math mode, a construct like A test$_\textnormal{subscript}$ will produce a subscript typeset in text mode, not math mode. Note that there are packages specialized for writing Chemical formulas such as mhchem.

Math symbols
LaTeX provides almost any mathematical symbol you’re likely to need. For example, if you include $\pi$ in your source, you will get the pi symbol π.
Below is a list of commonly-available symbols. It is by no means an exhaustive list. Each symbol here is described with a short phrase, and its symbol class (which determines the spacing around it) is given in parenthesis. The commands for these symbols can be used only in math mode.
\| 	∥ Parallel (relation). Synonym: \parallel.
\aleph 	ℵ Aleph, transfinite cardinal (ordinary).
\alpha 	α Lower case Greek letter alpha (ordinary).
\amalg 	⨿ Disjoint union (binary)
\angle 	∠ Geometric angle (ordinary). Similar: less-than sign < and angle bracket \langle.
\approx 	≈ Almost equal to (relation).
\ast 	∗ Asterisk operator, convolution, six-pointed (binary). Synonym: *, which is often a superscript or subscript, as in the Kleene star. Similar: \star, which is five-pointed, and is sometimes used as a general binary operation, and sometimes reserved for cross-correlation.
\asymp 	≍ Asymptomatically equivalent (relation).
\backslash 	\ Backslash (ordinary). Similar: set minus \setminus, and \textbackslash for backslash outside of math mode.
\beta 	β Lower case Greek letter beta (ordinary).
\bigcap 	⋂ Variable-sized, or n-ary, intersection (operator). Similar: binary intersection \cap.
\bigcirc 	⚪ Circle, larger (binary). Similar: function composition \circ.
\bigcup 	⋃ Variable-sized, or n-ary, union (operator). Similar: binary union \cup.
\bigodot 	⨀ Variable-sized, or n-ary, circled dot operator (operator).
\bigoplus 	⨁ Variable-sized, or n-ary, circled plus operator (operator).
\bigotimes 	⨂ Variable-sized, or n-ary, circled times operator (operator).
\bigtriangledown 	▽ Variable-sized, or n-ary, open triangle pointing down (operator).
\bigtriangleup 	△ Variable-sized, or n-ary, open triangle pointing up (operator).
\bigsqcup 	⨆ Variable-sized, or n-ary, square union (operator).
\biguplus 	⨄ Variable-sized, or n-ary, union operator with a plus (operator). (Note that the name has only one p.)
\bigvee 	⋁ Variable-sized, or n-ary, logical-and (operator).
\bigwedge 	⋀ Variable-sized, or n-ary, logical-or (operator).
\bot 	⊥ Up tack, bottom, least element of a poset, or a contradiction (ordinary). See also \top.
\bowtie 	⋈ Natural join of two relations (relation).
\Box 	□ Modal operator for necessity; square open box (ordinary). This is not available in Plain TeX. In LaTeX you need to load the amssymb package.
\bullet 	 • Bullet (binary). Similar: multiplication dot \cdot.
\cap 	∩ Intersection of two sets (binary). Similar: variable-sized operator \bigcap.
\cdot 	⋅ Multiplication (binary). Similar: Bullet dot \bullet.
\chi 	χ Lower case Greek chi (ordinary).
\circ 	∘ Function composition, ring operator (binary). Similar: variable-sized operator \bigcirc.
\clubsuit 	♣ Club card suit (ordinary).
\complement 	∁ Set complement, used as a superscript as in $S^\complement$ (ordinary). This is not available in Plain TeX. In LaTeX you should load the amssymb package. Also used: $S^{\mathsf{c}}$ or $\bar{S}$.
\cong 	≅ Congruent (relation).
\coprod 	∐ Coproduct (operator).
\cup 	∪ Union of two sets (binary). Similar: variable-sized operator \bigcup.
\dagger 	† Dagger relation (binary).
\dashv 	⊣ Dash with vertical, reversed turnstile (relation). Similar: turnstile \vdash.
\ddagger 	‡ Double dagger relation (binary).
\Delta 	Δ Greek upper case delta, used for increment (ordinary).
\delta 	δ Greek lower case delta (ordinary).
\Diamond 	◇ Large diamond operator (ordinary). This is not available in Plain TeX. In LaTeX you must load the amssymb package.
\diamond 	⋄ Diamond operator, or diamond bullet (binary). Similar: large diamond \Diamond, circle bullet \bullet.
\diamondsuit 	♢ Diamond card suit (ordinary).
\div 	÷ Division sign (binary).
\doteq 	≐ Approaches the limit (relation). Similar: geometrically equal to \Doteq.
\downarrow 	↓ Down arrow, converges (relation). Similar: double line down arrow \Downarrow.
\Downarrow 	⇓ Double line down arrow (relation). Similar: single line down arrow \downarrow.
\ell 	ℓ Lower-case cursive letter l (ordinary).
\emptyset 	∅ Empty set symbol (ordinary). Similar: reversed empty set \varnothing.
\epsilon 	ϵ Lower case Greek-text letter (ordinary). More widely used in mathematics is the curly epsilon \varepsilon ε. Related: the set membership relation \in ∈.
\equiv 	≡ Equivalence (relation).
\eta 	η Lower case Greek letter (ordinary).
\exists 	∃ Existential quantifier (ordinary).
\flat 	♭ Musical flat (ordinary).
\forall 	∀ Universal quantifier (ordinary).
\frown 	⌢ Downward curving arc (ordinary).
\Gamma 	Γ Upper case Greek letter (ordinary).
\gamma 	γ Lower case Greek letter (ordinary).
\ge 	≥ Greater than or equal to (relation). This is a synonym for \geq.
\geq 	≥ Greater than or equal to (relation). This is a synonym for \ge.
\gets 	← Is assigned the value (relation). Synonym: \leftarrow.
\gg 	≫ Much greater than (relation). Similar: much less than \ll.
\hbar 	ℏ Planck constant over two pi (ordinary).
\heartsuit 	♡ Heart card suit (ordinary).
\hookleftarrow 	↩ Hooked left arrow (relation).
\hookrightarrow 	↪ Hooked right arrow (relation).
\iff 	⟷ If and only if (relation). It is \Longleftrightarrow with a \thickmuskip on either side.
\Im 	ℑ Imaginary part (ordinary). See: real part \Re.
\in 	∈ Set element (relation). See also: lower case Greek letter epsilon \epsilonϵ and rounded small epsilon \varepsilon.
\infty 	∞ Infinity (ordinary).
\int 	∫ Integral (operator).
\iota 	ι Lower case Greek letter (ordinary).
\Join 	⨝ Condensed bowtie symbol (relation). Not available in Plain TeX.
\kappa 	κ Lower case Greek letter (ordinary).
\Lambda 	Λ Upper case Greek letter (ordinary).
\lambda 	λ Lower case Greek letter (ordinary).
\land 	∧ Logical and (binary). This is a synonym for \wedge. See also logical or \lor.
\langle 	⟨ Left angle, or sequence, bracket (opening). Similar: less-than <. Matches \rangle.
\lbrace 	{ Left curly brace (opening). Synonym: \{. Matches \rbrace.
\lbrack 	[ Left square bracket (opening). Synonym: [. Matches \rbrack.
\lceil 	⌈ Left ceiling bracket, like a square bracket but with the bottom shaved off (opening). Matches \rceil.
\le 	≤ Less than or equal to (relation). This is a synonym for \leq.
\leadsto 	⇝ Squiggly right arrow (relation). This is not available in Plain TeX. In LaTeX you should load the amssymb package. To get this symbol outside of math mode you can put \newcommand*{\Leadsto}{\ensuremath{\leadsto}} in the preamble and then use \Leadsto instead.
\Leftarrow 	⇐ Is implied by, double-line left arrow (relation). Similar: single-line left arrow \leftarrow.
\leftarrow 	← Single-line left arrow (relation). Synonym: \gets. Similar: double-line left arrow \Leftarrow.
\leftharpoondown 	↽ Single-line left harpoon, barb under bar (relation).
\leftharpoonup 	↼ Single-line left harpoon, barb over bar (relation).
\Leftrightarrow 	⇔ Bi-implication; double-line double-headed arrow (relation). Similar: single-line double headed arrow \leftrightarrow.
\leftrightarrow 	↔ Single-line double-headed arrow (relation). Similar: double-line double headed arrow \Leftrightarrow.
\leq 	≤ Less than or equal to (relation). This is a synonym for \le.
\lfloor 	⌊ Left floor bracket (opening).
\lhd 	◁ Arrowhead, that is, triangle, pointing left (binary). This is not available in Plain TeX. In LaTeX you should load the amssymb package. For the normal subgroup symbol you should load amssymb and use \vartriangleleft (which is a relation and so gives better spacing).
\ll 	≪ Much less than (relation). Similar: much greater than \gg.
\lnot 	¬ Logical negation (ordinary). Synonym: \neg.
\longleftarrow 	⟵ Long single-line left arrow (relation). Similar: long double-line left arrow \Longleftarrow.
\longleftrightarrow 	⟷ Long single-line double-headed arrow (relation). Similar: long double-line double-headed arrow \Longleftrightarrow.
\longmapsto 	⟼ Long single-line left arrow starting with vertical bar (relation). Similar: shorter version \mapsto.
\longrightarrow 	⟶ Long single-line right arrow (relation). Similar: long double-line right arrow \Longrightarrow.
\lor 	∨ Logical or (binary). Synonym: wedge \wedge.
\mapsto 	↦ Single-line left arrow starting with vertical bar (relation). Similar: longer version \longmapsto.
\mho 	℧ Conductance, half-circle rotated capital omega (ordinary). This is not available in Plain TeX. In LaTeX you should load the amssymb package.
\mid 	∣ Single-line vertical bar (relation). A typical use of \mid is for a set \{\, x \mid x\geq 5 \,\}.
Similar: \vert and | produce the same single-line vertical bar symbol but without any spacing (they fall in class ordinary) and you should not use them as relations but instead only as ordinals, i.e., footnote symbols. For absolute value, see the entry for \vert and for norm see the entry for \Vert.
\models 	⊨ Entails, or satisfies; double turnstile, short double dash (relation). Similar: long double dash \vDash.
\mp 	∓ Minus or plus (relation).
\mu 	μ Lower case Greek letter (ordinary).
\nabla 	∇ Hamilton’s del, or differential, operator (ordinary).
\natural 	♮ Musical natural notation (ordinary).
\ne 	≠ Not equal (relation). Synonym: \neq.
\nearrow 	↗ North-east arrow (relation).
\neg 	¬ Logical negation (ordinary). Synonym: \lnot. Sometimes instead used for negation: \sim.
\neq 	≠ Not equal (relation). Synonym: \ne.
\ni 	∋ Reflected membership epsilon; has the member (relation). Synonym: \owns. Similar: is a member of \in.
\not 	  ̸ Long solidus, or slash, used to overstrike a following operator (relation).
Many negated operators that don’t require \not are available, particularly with the amssymb package. For example, \notin is probably typographically preferable to \not\in.
\notin 	∉ Not an element of (relation). Similar: not subset of \nsubseteq.
\nu 	ν Lower case Greek letter (ordinary).
\nwarrow 	↖ North-west arrow (relation).
\odot 	⊙ Dot inside a circle (binary). Similar: variable-sized operator \bigodot.
\oint 	∮ Contour integral, integral with circle in the middle (operator).
\Omega 	Ω Upper case Greek letter (ordinary).
\omega 	ω Lower case Greek letter (ordinary).
\ominus 	⊖ Minus sign, or dash, inside a circle (binary).
\oplus 	⊕ Plus sign inside a circle (binary). Similar: variable-sized operator \bigoplus.
\oslash 	⊘ Solidus, or slash, inside a circle (binary).
\otimes 	⊗ Times sign, or cross, inside a circle (binary). Similar: variable-sized operator \bigotimes.
\owns 	∋ Reflected membership epsilon; has the member (relation). Synonym: \ni. Similar: is a member of \in.
\parallel 	∥ Parallel (relation). Synonym: \|.
\partial 	∂ Partial differential (ordinary).
\perp 	⟂ Perpendicular (relation). Similar: \bot uses the same glyph but the spacing is different because it is in the class ordinary.
\phi 	ϕ Lower case Greek letter (ordinary). The variant form is \varphi φ.
\Pi 	Π Upper case Greek letter (ordinary).
\pi 	π Lower case Greek letter (ordinary). The variant form is \varpi ϖ.
\pm 	± Plus or minus (binary).
\prec 	≺ Preceeds (relation). Similar: less than <.
\preceq 	⪯ Preceeds or equals (relation). Similar: less than or equals \leq.
\prime 	′ Prime, or minute in a time expression (ordinary). Typically used as a superscript $A^\prime$. Note that $f^\prime$ and $f'$ produce the same result. An advantage of the second is that $f'''$ produces the the desired symbol, that is, the same result as $f^{\prime\prime\prime}$, but uses somewhat less typing. Note that you can only use \prime in math mode but you can type right single quote ' in text mode also, although it resuts in a different look than in math mode.
\prod 	∏ Product (operator).
\propto 	∝ Is proportional to (relation)
\Psi 	Ψ Upper case Greek letter (ordinary).
\psi 	ψ Lower case Greek letter (ordinary).
\rangle 	➹ Right angle, or sequence, bracket (closing). Similar: greater than >. Matches:\langle.
\rbrace 	} Right curly brace (closing). Synonym: \}. Matches \lbrace.
\rbrack 	] Right square bracket (closing). Synonym: ]. Matches \lbrack.
\rceil 	⌉ Right ceiling bracket (closing). Matches \lceil.
\Re 	ℜ Real part, real numbers, cursive capital R (ordinary). Related: double-line, or blackboard bold, R \mathbb{R}; to access this, load the amsfonts package.
\restriction 	↾ Restriction of a function (relation). Synonym: \upharpoonright. Not available in Plain TeX. In LaTeX you should load the amssymb package.
\rfloor 	⌋ Right floor bracket, a right square bracket with the top cut off (closing). Matches \lfloor.
\rhd 	◁ Arrowhead, that is, triangle, pointing right (binary). This is not available in Plain TeX. In LaTeX you should load the amssymb package. For the normal subgroup symbol you should instead load amssymb and use \vartriangleright (which is a relation and so gives better spacing).
\rho 	ρ Lower case Greek letter (ordinary). The variant form is \varrho ϱ.
\Rightarrow 	⇒ Implies, right-pointing double line arrow (relation). Similar: right single-line arrow \rightarrow.
\rightarrow 	→ Right-pointing single line arrow (relation). Synonym: \to. Similar: right double line arrow \Rightarrow.
\rightharpoondown 	⇁ Right-pointing harpoon with barb below the line (relation).
\rightharpoonup 	⇀ Right-pointing harpoon with barb above the line (relation).
\rightleftharpoons 	⇌ Right harpoon up above left harpoon down (relation).
\searrow 	↘ Arrow pointing southeast (relation).
\setminus 	⧵ Set difference, reverse solidus or slash, like \ (binary). Similar: backslash \backslash and also \textbackslash outside of math mode.
\sharp 	♯ Musical sharp (ordinary).
\Sigma 	Σ Upper case Greek letter (ordinary).
\sigma 	σ Lower case Greek letter (ordinary). The variant form is \varsigma ς.
\sim 	∼ Similar, in a relation (relation).
\simeq 	≃ Similar or equal to, in a relation (relation).
\smallint 	∫ Integral sign that does not change to a larger size in a display (operator).
\smile 	⌣ Upward curving arc (ordinary).
\spadesuit 	♠ Spade card suit (ordinary).
\sqcap 	⊓ Square intersection symbol (binary). Similar: intersection cap.
\sqcup 	⊔ Square union symbol (binary). Similar: union cup. Related: variable-sized operator \bigsqcup.
\sqsubset 	⊏ Square subset symbol (relation). Similar: subset \subset. This is not available in Plain TeX. In LaTeX you should load the amssymb package.
\sqsubseteq 	⊑ Square subset or equal symbol (binary). Similar: subset or equal to \subseteq.
\sqsupset 	⊐ Square superset symbol (relation). Similar: superset \supset. This is not available in Plain TeX. In LaTeX you should load the amssymb package.
\sqsupseteq 	⊒ Square superset or equal symbol (binary). Similar: superset or equal \supseteq.
\star 	⋆ Five-pointed star, sometimes used as a general binary operation but sometimes reserved for cross-correlation (binary). Similar: the synonyms asterisk * and \ast, which are six-pointed, and more often appear as a superscript or subscript, as with the Kleene star.
\subset 	⊂ Subset (occasionally, is implied by) (relation).
\subseteq 	⊆ Subset or equal to (relation).
\succ 	≻ Comes after, succeeds (relation). Similar: is less than >.
\succeq 	⪰ Succeeds or is equal to (relation). Similar: less than or equal to \leq.
\sum 	∑ Summation (operator). Similar: Greek capital sigma \Sigma.
\supset 	⊃ Superset (relation).
\supseteq 	⊇ Superset or equal to (relation).
\surd 	√ Radical symbol (ordinary). The LaTeX command \sqrt{..} typesets the square root of the argument, with a bar that extends to cover the argument.
\swarrow 	↙ Southwest-pointing arrow (relation).
\tau 	τ Lower case Greek letter (ordinary).
\theta 	θ Lower case Greek letter (ordinary). The variant form is \vartheta ϑ.
\times 	× Primary school multiplication sign (binary). See also \cdot.
\to 	→ Right-pointing single line arrow (relation). Synonym: \rightarrow.
\top 	⊤ Top, greatest element of a poset (ordinary). See also \bot.
\triangle 	△ Triangle (ordinary).
\triangleleft 	◁ Not-filled triangle pointing left (binary). Similar: \lhd. For the normal subgroup symbol you should load amssymb and use \vartriangleleft (which is a relation and so gives better spacing).
\triangleright 	▷ Not-filled triangle pointing right (binary). For the normal subgroup symbol you should instead load amssymb and use \vartriangleright (which is a relation and so gives better spacing).
\unlhd 	⊴ Left-pointing not-filled arrowhead, that is, triangle, with a line under (binary). This is not available in Plain TeX. In LaTeX you should load the amssymb package. For the normal subgroup symbol load amssymb and use \vartrianglelefteq (which is a relation and so gives better spacing).
\unrhd 	⊵ Right-pointing not-filled arrowhead, that is, triangle, with a line under (binary). This is not available in Plain TeX. In LaTeX you should load the amssymb package. For the normal subgroup symbol load amssymb and use \vartrianglerighteq (which is a relation and so gives better spacing).
\Uparrow 	⇑ Double-line upward-pointing arrow (relation). Similar: single-line up-pointing arrow \uparrow.
\uparrow 	↑ Single-line upward-pointing arrow, diverges (relation). Similar: double-line up-pointing arrow \Uparrow.
\Updownarrow 	⇕ Double-line upward-and-downward-pointing arrow (relation). Similar: single-line upward-and-downward-pointing arrow \updownarrow.
\updownarrow 	↕ Single-line upward-and-downward-pointing arrow (relation). Similar: double-line upward-and-downward-pointing arrow \Updownarrow.
\upharpoonright 	↾ Up harpoon, with barb on right side (relation). Synonym: \restriction. Not available in Plain TeX. In LaTeX you should load the amssymb package.
\uplus 	⊎ Multiset union, a union symbol with a plus symbol in the middle (binary). Similar: union \cup. Related: variable-sized operator \biguplus.
\Upsilon 	Υ Upper case Greek letter (ordinary).
\upsilon 	υ Lower case Greek letter (ordinary).
\varepsilon 	ε Rounded small epsilon (ordinary). This is more widely used in mathematics than the non-variant lower case Greek-text letter form \epsilon ϵ. Related: set membership \in.
\varphi 	φ Variant on the lower case Greek letter (ordinary). The non-variant form is \phi ϕ.
\varpi 	ϖ Variant on the lower case Greek letter (ordinary). The non-variant form is \pi π.
\varrho 	ϱ Variant on the lower case Greek letter (ordinary). The non-variant form is \rho ρ.
\varsigma 	ς Variant on the lower case Greek letter (ordinary). The non-variant form is \sigma σ.
\vartheta 	ϑ Variant on the lower case Greek letter (ordinary). The non-variant form is \theta θ.
\vdash 	⊢ Provable; turnstile, vertical and a dash (relation). Similar: turnstile rotated a half-circle \dashv.
\vee 	∨ Logical or; a downwards v shape (binary). Related: logical and \wedge. Similar: variable-sized operator \bigvee.
\Vert 	‖ Vertical double bar (ordinary). Similar: vertical single bar \vert.
For a norm you can use the mathtools package and add \DeclarePairedDelimiter\norm{\lVert}{\rVert} to your preamble. This gives you three command variants for double-line vertical bars that are correctly horizontally spaced: if in the document body you write the starred version $\norm*{M^\perp}$ then the height of the vertical bars will match the height of the argument, whereas with \norm{M^\perp} the bars do not grow with the height of the argument but instead are the default height, and \norm[size command]{M^\perp} also gives bars that do not grow but are set to the size given in the size command, e.g., \Bigg.
\vert 	| Single line vertical bar (ordinary). Similar: double-line vertical bar \Vert. For such that, as in the definition of a set, use \mid because it is a relation.
For absolute value you can use the mathtools package and add \DeclarePairedDelimiter\abs{\lvert}{\rvert} to your preamble. This gives you three command variants for single-line vertical bars that are correctly horizontally spaced: if in the document body you write the starred version $\abs*{\frac{22}{7}}$ then the height of the vertical bars will match the height of the argument, whereas with \abs{\frac{22}{7}} the bars do not grow with the height of the argument but instead are the default height, and \abs[size command]{\frac{22}{7}} also gives bars that do not grow but are set to the size given in the size command, e.g., \Bigg.
\wedge 	∧ Logical and (binary). Synonym: \land. See also logical or \vee. Similar: variable-sized operator \bigwedge.
\wp 	℘ Weierstrass p (ordinary).
\wr 	≀ Wreath product (binary).
\Xi 	Ξ Upper case Greek letter (ordinary).
\xi 	ξ Lower case Greek letter (ordinary).
\zeta 	ζ Lower case Greek letter (ordinary).

Math functions
These commands produce roman function names in math mode with proper spacing.
\arccos 	\arccos
\arcsin 	\arcsin
\arctan 	\arctan
\arg 	\arg
\bmod 	Binary modulo operator (x \bmod y)
\cos 	\cos
\cosh 	\cosh
\cot 	\cot
\coth 	\coth
\csc 	\csc
\deg 	\deg
\det 	\det
\dim 	\dim
\exp 	\exp
\gcd 	\gcd
\hom 	\hom
\inf 	\inf
\ker 	\ker
\lg 	\lg
\lim 	\lim
\liminf 	\liminf
\limsup 	\limsup
\ln 	\ln
\log 	\log
\max 	\max
\min 	\min
\pmod 	parenthesized modulus, as in (\pmod 2^n - 1)
\Pr 	\Pr
\sec 	\sec
\sin 	\sin
\sinh 	\sinh
\sup 	sup
\tan 	\tan
\tanh 	\tanh

Math accents
LaTeX provides a variety of commands for producing accented letters in math. These are different from accents in normal text (see Accents).
\acute 	 Math acute accent: \acute{x}.
\bar 	 Math bar-over accent: \bar{x}.
\breve 	 Math breve accent: \breve{x}.
\check 	 Math háček (check) accent: \check{x}.
\ddot 	 Math dieresis accent: \ddot{x}.
\dot 	 Math dot accent: \dot{x}.
\grave 	 Math grave accent: \grave{x}.
\hat 	 Math hat (circumflex) accent: \hat{x}.
\imath 	 Math dotless i.
\jmath 	 Math dotless j.
\mathring 	 Math ring accent: x*.
\tilde 	 Math tilde accent: \tilde{x}.
\vec 	 Math vector symbol: \vec{x}.
\widehat 	 Math wide hat accent: \widehat{x+y}.
\widetilde 	 Math wide tilde accent: \widetilde{x+y}.

Spacing in math mode
In a math environment, LaTeX ignores the spaces that you use in the source, and instead puts in the spacing according to the normal rules for mathematics texts.
Many math mode spacing definitions are expressed in terms of the math unit mu given by 1 em = 18 mu, where the em is taken from the current math symbols family (see Units of length). LaTeX provides the following commands for use in math mode:
\; 	 Normally 5.0mu plus 5.0mu. The longer name is \thickspace. Math mode only.
\: 	\> 	 Normally 4.0mu plus 2.0mu minus 4.0mu. The longer name is \medspace. Math mode only.
\, 	 Normally 3mu. The longer name is \thinspace. This can be used in both math mode and text mode.
\! 	 A negative thin space. Normally -3mu. Math mode only.
\quad 	 This is 18mu, that is, 1em. This is often used for space surrounding equations or expressions, for instance for the space between two equations inside a displaymath environment. It is available in both text and math mode.
\qquad 	 A length of 2 quads, that is, 36mu = 2em. It is available in both text and math mode.
In this example a thinspace separates the function from the infinitesimal.

\int_0^1 f(x)\,dx

Math miscellany
\* 	 A “discretionary” multiplication symbol, at which a line break is allowed.
\cdots 	A horizontal ellipsis with the dots raised to the center of the line.
\ddots 	A diagonal ellipsis: \ddots.
\frac{num}{den} 	 Produces the fraction num divided by den.
\left delim1 ... \right delim2 	 The two delimiters need not match; ‘.’ acts as a null delimiter, producing no output. The delimiters are sized according to the math in between. Example: \left( \sum_i=1^10 a_i \right].
\overbrace{text} 	Generates a brace over text. For example, \overbrace{x+\cdots+x}^{k \rm\;times}.
\overline{text} 	Generates a horizontal line over tex. For example, \overline{x+y}.
\sqrt[root]{arg} 	Produces the representation of the square root of arg. The optional argument root determines what root to produce. For example, the cube root of x+y would be typed as $\sqrt[3]{x+y}$.
\stackrel{text}{relation} 	Puts text above relation. For example, \stackrel{f}{\longrightarrow}.
\underbrace{math} 	Generates math with a brace underneath.
\underline{text} 	Causes text, which may be either math mode or not, to be underlined. The line is always below the text, taking account of descenders.
\vdots 	 Produces a vertical ellipsis.