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Functions, symbols, special characters

Accents/diacritics
\acute{a} \grave{a} \hat{a} \tilde{a} \breve{a}	<math>\acute{a} \grave{a} \hat{a} \tilde{a} \breve{a}\,\!</math>
\check{a} \bar{a} \ddot{a} \dot{a}	<math>\check{a} \bar{a} \ddot{a} \dot{a}\!</math>
Standard functions
\sin a \cos b \tan c	<math>\sin a \cos b \tan c\!</math>
\sec d \csc e \cot f	<math>\sec d \csc e \cot f\,\!</math>
\arcsin h \arccos i \arctan j	<math>\arcsin h \arccos i \arctan j\,\!</math>
\sinh k \cosh l \tanh m \coth n\!	<math>\sinh k \cosh l \tanh m \coth n\!</math>
\operatorname{sh}\,o\,\operatorname{ch}\,p\,\operatorname{th}\,q\!	<math>\operatorname{sh}\,o\,\operatorname{ch}\,p\,\operatorname{th}\,q\!</math>
\operatorname{arsinh}\,r\,\operatorname{arcosh}\,s\,\operatorname{artanh}\,t	<math>\operatorname{arsinh}\,r\,\operatorname{arcosh}\,s\,\operatorname{artanh}\,t\,\!</math>
\lim u \limsup v \liminf w \min x \max y\!	<math>\lim u \limsup v \liminf w \min x \max y\!</math>
\inf z \sup a \exp b \ln c \lg d \log e \log_{10} f \ker g\!	<math>\inf z \sup a \exp b \ln c \lg d \log e \log_{10} f \ker g\!</math>
\deg h \gcd i \Pr j \det k \hom l \arg m \dim n	<math>\deg h \gcd i \Pr j \det k \hom l \arg m \dim n\!</math>
Modular arithmetic
s_k \equiv 0 \pmod{m}	<math>s_k \equiv 0 \pmod{m}\,\!</math>
a\,\bmod\,b	<math>a\,\bmod\,b\,\!</math>
\mid \; \nmid	<math> \mid \; \nmid \!</math>
Derivatives
\nabla \, \partial x \, dx \, \dot x \, \ddot y\, dy/dx\, \frac{dy}{dx}\, \frac{\partial^2 y}{\partial x_1\,\partial x_2}	<math>\nabla \, \partial x \, dx \, \dot x \, \ddot y\, dy/dx\, \frac{dy}{dx}\, \frac{\partial^2 y}{\partial x_1\,\partial x_2}</math>
Sets
\forall \exists \empty \emptyset \varnothing	<math>\forall \exists \empty \emptyset \varnothing\,\!</math>
\in \ni \not \in \notin \subset \subseteq \supset \supseteq	<math>\in \ni \not \in \notin \subset \subseteq \supset \supseteq\,\!</math>
\cap \bigcap \cup \bigcup \biguplus \setminus \smallsetminus	<math>\cap \bigcap \cup \bigcup \biguplus \setminus \smallsetminus\,\!</math>
\sqsubset \sqsubseteq \sqsupset \sqsupseteq \sqcap \sqcup \bigsqcup	<math>\sqsubset \sqsubseteq \sqsupset \sqsupseteq \sqcap \sqcup \bigsqcup\,\!</math>
Operators
+ \oplus \bigoplus \pm \mp -	<math>+ \oplus \bigoplus \pm \mp - \,\!</math>
\times \otimes \bigotimes \cdot \circ \bullet \bigodot	<math>\times \otimes \bigotimes \cdot \circ \bullet \bigodot\,\!</math>
\star * / \div \frac{1}{2}	<math>\star * / \div \frac{1}{2}\,\!</math>
Logic
\land (or \and) \wedge \bigwedge \bar{q} \overline{q} \to \And	<math>\land \wedge \bigwedge \bar{q} \ \overline{q} \to \And\,\!</math>
\lor \vee \bigvee \lnot \neg q \leftrightarrow	<math>\lor \vee \bigvee \lnot \, \neg q \leftrightarrow\,\!</math>
Root
\sqrt{2} \sqrt[n]{x}	<math>\sqrt{2} \sqrt[n]{x}\,\!</math>
Relations
\sim \approx \simeq \cong \dot= \overset{\underset{\mathrm{def}}{}}{=}	<math>\sim \approx \simeq \cong \dot= \overset{\underset{\mathrm{def}}{}}{=}\,\!</math>
\le < \ll \gg \ge > \equiv \not\equiv \ne \mbox{or} \neq \propto	<math>\le < \ll \gg \ge > \equiv \not\equiv \ne \mbox{or} \neq \propto\,\!</math>
Geometric
\Diamond \Box \triangle \angle \perp \| 45^\circ	45^\circ\,\!</math>
Arrows
\leftarrow (or \gets) \rightarrow (or \to) \nleftarrow \nrightarrow \leftrightarrow \nleftrightarrow \longleftarrow \longrightarrow \longleftrightarrow	<math>\leftarrow \rightarrow \nleftarrow \not\to \leftrightarrow \nleftrightarrow \longleftarrow \longrightarrow \longleftrightarrow \,\!</math>
\Leftarrow \Rightarrow \nLeftarrow \nRightarrow \Leftrightarrow \nLeftrightarrow \Longleftarrow \Longrightarrow \Longleftrightarrow (or \iff)	<math>\Leftarrow \Rightarrow \nLeftarrow \nRightarrow \Leftrightarrow \nLeftrightarrow \Longleftarrow \Longrightarrow \Longleftrightarrow \!</math>
\uparrow \downarrow \updownarrow \Uparrow \Downarrow \Updownarrow \nearrow \searrow \swarrow \nwarrow	<math>\uparrow \downarrow \updownarrow \Uparrow \Downarrow \Updownarrow \nearrow \searrow \swarrow \nwarrow \!</math>
\rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft \upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \leftrightharpoons	<math>\rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft \upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \leftrightharpoons \,\!</math>
\curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \Rrightarrow \rightarrowtail \looparrowright	<math>\curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \Rrightarrow \rightarrowtail \looparrowright \,\!</math>
\curvearrowright \circlearrowright \Rsh \downdownarrows \leftleftarrows \leftrightarrows \Lleftarrow \leftarrowtail \looparrowleft	<math>\curvearrowright \circlearrowright \Rsh \downdownarrows \leftleftarrows \leftrightarrows \Lleftarrow \leftarrowtail \looparrowleft \,\!</math>
\mapsto \longmapsto \hookrightarrow \hookleftarrow \multimap \leftrightsquigarrow \rightsquigarrow \twoheadrightarrow \twoheadleftarrow	<math>\mapsto \longmapsto \hookrightarrow \hookleftarrow \multimap \leftrightsquigarrow \rightsquigarrow \twoheadrightarrow \twoheadleftarrow\,\!</math>
Special
\And \eth \S \P \% \dagger \ddagger \ldots \cdots	<math>\And \eth \S \P \% \dagger \ddagger \ldots \cdots\,\!</math>
\smile \frown \wr \triangleleft \triangleright \infty \bot \top	<math>\smile \frown \wr \triangleleft \triangleright \infty \bot \top\,\!</math>
\vdash \vDash \Vdash \models \lVert \rVert \imath \hbar	<math>\vdash \vDash \Vdash \models \lVert \rVert \imath \hbar\,\!</math>
\ell \mho \Finv \Re \Im \wp \complement	<math>\ell \mho \Finv \Re \Im \wp \complement\,\!</math>
\diamondsuit \heartsuit \clubsuit \spadesuit \Game \flat \natural \sharp	<math>\diamondsuit \heartsuit \clubsuit \spadesuit \Game \flat \natural \sharp\,\!</math>
Unsorted (new stuff)
\vartriangle \triangledown \lozenge \circledS \measuredangle \nexists \Bbbk \backprime \blacktriangle \blacktriangledown	<math> \vartriangle \triangledown \lozenge \circledS \measuredangle \nexists \Bbbk \backprime \blacktriangle \blacktriangledown</math>
\blacksquare \blacklozenge \bigstar \sphericalangle \diagup \diagdown \dotplus \Cap \Cup \barwedge	<math> \blacksquare \blacklozenge \bigstar \sphericalangle \diagup \diagdown \dotplus \Cap \Cup \barwedge\!</math>
\veebar \doublebarwedge \boxminus \boxtimes \boxdot \boxplus \divideontimes \ltimes \rtimes \leftthreetimes	<math> \veebar \doublebarwedge \boxminus \boxtimes \boxdot \boxplus \divideontimes \ltimes \rtimes \leftthreetimes</math>
\rightthreetimes \curlywedge \curlyvee \circleddash \circledast \circledcirc \centerdot \intercal \leqq \leqslant	<math> \rightthreetimes \curlywedge \curlyvee \circleddash \circledast \circledcirc \centerdot \intercal \leqq \leqslant</math>
\eqslantless \lessapprox \approxeq \lessdot \lll \lessgtr \lesseqgtr \lesseqqgtr \doteqdot \risingdotseq	<math> \eqslantless \lessapprox \approxeq \lessdot \lll \lessgtr \lesseqgtr \lesseqqgtr \doteqdot \risingdotseq</math>
\fallingdotseq \backsim \backsimeq \subseteqq \Subset \preccurlyeq \curlyeqprec \precsim \precapprox \vartriangleleft	<math> \fallingdotseq \backsim \backsimeq \subseteqq \Subset \preccurlyeq \curlyeqprec \precsim \precapprox \vartriangleleft</math>
\Vvdash \bumpeq \Bumpeq \geqq \geqslant \eqslantgtr \gtrsim \gtrapprox \eqsim \gtrdot	<math> \Vvdash \bumpeq \Bumpeq \geqq \geqslant \eqslantgtr \gtrsim \gtrapprox \eqsim \gtrdot</math>
\ggg \gtrless \gtreqless \gtreqqless \eqcirc \circeq \triangleq \thicksim \thickapprox \supseteqq	<math> \ggg \gtrless \gtreqless \gtreqqless \eqcirc \circeq \triangleq \thicksim \thickapprox \supseteqq</math>
\Supset \succcurlyeq \curlyeqsucc \succsim \succapprox \vartriangleright \shortmid \shortparallel \between \pitchfork	<math> \Supset \succcurlyeq \curlyeqsucc \succsim \succapprox \vartriangleright \shortmid \shortparallel \between \pitchfork</math>
\varpropto \blacktriangleleft \therefore \backepsilon \blacktriangleright \because \nleqslant \nleqq \lneq \lneqq	<math> \varpropto \blacktriangleleft \therefore \backepsilon \blacktriangleright \because \nleqslant \nleqq \lneq \lneqq</math>
\lvertneqq \lnsim \lnapprox \nprec \npreceq \precneqq \precnsim \precnapprox \nsim \nshortmid	<math> \lvertneqq \lnsim \lnapprox \nprec \npreceq \precneqq \precnsim \precnapprox \nsim \nshortmid</math>
\nvdash \nVdash \ntriangleleft \ntrianglelefteq \nsubseteq \nsubseteqq \varsubsetneq \subsetneqq \varsubsetneqq \ngtr	<math> \nvdash \nVdash \ntriangleleft \ntrianglelefteq \nsubseteq \nsubseteqq \varsubsetneq \subsetneqq \varsubsetneqq \ngtr</math>
\subsetneq	<math>\subsetneq</math>
\ngeqslant \ngeqq \gneq \gneqq \gvertneqq \gnsim \gnapprox \nsucc \nsucceq \succneqq	<math> \ngeqslant \ngeqq \gneq \gneqq \gvertneqq \gnsim \gnapprox \nsucc \nsucceq \succneqq</math>
\succnsim \succnapprox \ncong \nshortparallel \nparallel \nvDash \nVDash \ntriangleright \ntrianglerighteq \nsupseteq	<math> \succnsim \succnapprox \ncong \nshortparallel \nparallel \nvDash \nVDash \ntriangleright \ntrianglerighteq \nsupseteq</math>
\nsupseteqq \varsupsetneq \supsetneqq \varsupsetneqq	<math> \nsupseteqq \varsupsetneq \supsetneqq \varsupsetneqq</math>
\jmath \surd \ast \uplus \diamond \bigtriangleup \bigtriangledown \ominus	<math>\jmath \surd \ast \uplus \diamond \bigtriangleup \bigtriangledown \ominus\,\!</math>
\oslash \odot \bigcirc \amalg \prec \succ \preceq \succeq	<math>\oslash \odot \bigcirc \amalg \prec \succ \preceq \succeq\,\!</math>
\dashv \asymp \doteq \parallel	<math>\dashv \asymp \doteq \parallel\,\!</math>
\ulcorner \urcorner \llcorner \lrcorner	<math>\ulcorner \urcorner \llcorner \lrcorner</math>

For a little more semantics on these symbols, see the brief TeX Cookbook