Feature	Syntax	How it looks rendered
std. functions (good)	sin x + \ln y +\operatorname{sgn} z\	{TEX()} {\sin x + \ln y +\operatorname{sgn} z} {TEX}
std. functions (wrong)	sin x + ln y + sgn z	{TEX()} {sin x + ln y + sgn z\,} {TEX}
Modular arithm.	{s_k \equiv 0 \pmod{m	{TEX()} {s_k \equiv 0 \pmod{m}} {TEX}
Derivatives	nabla \partial x dx \dot x \ddot y\	{TEX()} {\nabla \ \partial x \ dx \ \dot x\ \ddot y} {TEX}
Sets	\forall x \not\in \varnothing \subseteq A \cap B \cup \exists \{x,y\} \times C	{TEX()} {\forall x \not\in \varnothing \subseteq A \cap B \cup \exists \{x,y\} \times C} {TEX}
Logic	p \land \bar{q} \to p\lor \lnot q	{TEX()} {p \land \bar{q} \to p\lor \lnot q} {TEX}
Root	sqrt{2}\approx 1.4\	{TEX()} {\sqrt{2}\approx 1.4} {TEX}
	~np~ {sqrt[n]{x\ ~/np~	{TEX()} {\sqrt[n]{x}} {TEX}
Relations	sim \simeq \cong \le \ge \equiv \not\equiv \approx \ne\	{TEX()} {\sim \ \simeq \ \cong \ \le \ \ge \ \equiv \ \not\equiv \ \approx \ \ne} {TEX}
Geometric	~np~ triangle \angle \perp \| 45^\circ\ ~/np~	{TEX()} {\triangle \ \angle \perp \| \ 45^\circ} {TEX}
Arrows	\leftarrow \rightarrow \leftrightarrow \longleftarrow \longrightarrow \mapsto \longmapsto \nearrow \searrow \swarrow \nwarrow \uparrow \downarrow \updownarrow	{TEX()} {\leftarrow\ \rightarrow\ \leftrightarrow} {TEX} {TEX()} {\longleftarrow\ \longrightarrow} {TEX} {TEX()} {\mapsto\ \longmapsto} {TEX} {TEX()} {\nearrow\ \searrow\ \swarrow\ \nwarrow} {TEX} {TEX()} {\uparrow\ \downarrow\ \updownarrow} {TEX}
	\Leftarrow \Rightarrow \Leftrightarrow \Longleftarrow \Longrightarrow \Longleftrightarrow \Uparrow \Downarrow \Updownarrow	{TEX()} {\Leftarrow\ \Rightarrow\ \Leftrightarrow} {TEX} {TEX()} {\Longleftarrow\ \Longrightarrow\ \Longleftrightarrow} {TEX} {TEX()} {\Uparrow\ \Downarrow\ \Updownarrow} {TEX}
Special	\oplus \otimes \pm \mp \hbar \dagger \ddagger \star * \ldots \circ \cdot \times \bullet \infty \vdash \models	{TEX()} {\oplus \otimes \pm \mp \hbar \dagger \ddagger \star * \ldots} {TEX} {TEX()} {\circ \cdot \times \bullet\ \infty \ \vdash \ \models} {TEX}

!Subscripts, superscripts

Feature	Syntax	How it looks rendered
Superscript	~np~a^2 ~/np~	{TEX()} {a^2} {TEX}	{TEX()} {a^2} {TEX}
Subscript	a_2	{TEX()} {a_2} {TEX}	{TEX()} {a_2 \,\!} {TEX}
Grouping	~np~ {a^{2+2 ~/np~	{TEX()} {a^{2+2}} {TEX}	{TEX()} {a^{2+2} \,\!} {TEX}
	{a_{i,j	{TEX()} {a_{i,j}} {TEX}	{TEX()} {a_{i,j} \,\!} {TEX}
Combining sub & super	~np~ x_2^3 ~/np~	{TEX()} {x_2^3} {TEX}
Preceding sub & super	~np~ {}_1^2\!X_3^4 ~/np~	{TEX()} {{}_1^2\!X_3^4} {TEX}
Derivative (good)	'x	{TEX()} {x'} {TEX}	{TEX()} {x' \,\!} {TEX}
Derivative (wrong in HTML)	~np~ x^\prime~/np~	{TEX()} {x^\prime} {TEX}	{TEX()} {x^\prime \,\!} {TEX}
Derivative (wrong in PNG)	~np~ x\prime ~/np~	{TEX()} {x\prime} {TEX}	{TEX()} {x\prime \,\!} {TEX}
Derivative dots	{dot{x}, \ddot{x\	{TEX()} {\dot{x}, \ddot{x}} {TEX}
Underlines & overlines	\{hat a \bar b \vec c \widehat {d e f} \overline {g h i} \underline {j k l	{TEX()} {\hat a \ \bar b \ \vec c \ \widehat {d e f} \ \overline {g h i} \ \underline {j k l}} {TEX}
Sum	~np~ sum_{k=1}^N k^2\ ~/np~	{TEX()} {\sum_{k=1}^N k^2} {TEX}
Product	~np~ prod_{i=1}^N x_i\ ~/np~	{TEX()} {\prod_{i=1}^N x_i} {TEX}
Limit	lim_{n \to \infty}x_n\	{TEX()} {\lim_{n \to \infty}x_n} {TEX}
Integral	~np~ int_{-N}^{N} e^x\, dx\ ~/np~	{TEX()} {\int_{-N}^{N} e^x\, dx} {TEX}
Path Integral	~np~ oint_{C} x^3\, dx + 4y^2\, dy\ ~/np~	{TEX()} {\oint_{C} x^3\, dx + 4y^2\, dy} {TEX}

!Fractions, matrices, multilines

Feature	Syntax	How it looks rendered
Fractions	{frac{2}{4} or {2 \over 4\	{TEX()} {\frac{2}{4}} {TEX}
Binomial coefficients	{n \choose k}	{TEX()} {{n \choose k}} {TEX}
Small Fractions	{begin{matrix} \frac{2}{4} \end{matrix\	{TEX()} {\begin{matrix} \frac{2}{4} \end{matrix}} {TEX}
Matrices	{begin{matrix} x & y \\ z & v \end{matrix\	{TEX()} {\begin{matrix} x & y \\ z & v \end{matrix}} {TEX}
	{begin{vmatrix} x & y \\ z & v \end{vmatrix\	{TEX()} {\begin{vmatrix} x & y \\ z & v \end{vmatrix}} {TEX}
	{begin{Vmatrix} x & y \\ z & v \end{Vmatrix\	{TEX()} {\begin{Vmatrix} x & y \\ z & v \end{Vmatrix}} {TEX}
	\begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0\end{bmatrix}	{TEX()} {\begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0\end{bmatrix} } {TEX}
	{begin{Bmatrix} x & y \\ z & v \end{Bmatrix\	{TEX()} {\begin{Bmatrix} x & y \\ z & v \end{Bmatrix}} {TEX}
	{begin{pmatrix} x & y \\ z & v \end{pmatrix\	{TEX()} {\begin{pmatrix} x & y \\ z & v \end{pmatrix}} {TEX}
Case distinctions	f(n) = \left \{ \begin{matrix} n/2, & \mbox{if }n\mbox{ is even} \\ 3n+1, & \mbox{if }n\mbox{ is odd} \end{matrix} \right.	{TEX()} {f(n) = \left \{ \begin{matrix} n/2, & \mbox{if }n\mbox{ is even} \\ 3n+1, & \mbox{if }n\mbox{ is odd} \end{matrix} \right. } {TEX}
Multiline equations	~np~ \begin{matrix}f(n+1) & = & (n+1)^2 \\ \ & = & n^2 + 2n + 1 \end{matrix} ~/np~	{TEX()} {\begin{matrix}f(n+1) & = & (n+1)^2 \\ \ & = & n^2 + 2n + 1 \end{matrix}} {TEX}
Alternative multiline equations (using tables)	{| |- |{TEX()} {f(n+1)} {TEX} |{TEX()} {(n+1)^2} {TEX} |- | |{TEX()} {=n^2 + 2n + 1} {TEX} |}	{| |- |{TEX()} {f(n+1) \,\!} {TEX} |{TEX()} {(n+1)^2 \,\!} {TEX} |- | |{TEX()} {=n^2 + 2n + 1 \,\!} {TEX} |}

!Fonts

Feature	Syntax	How it looks rendered
Greek letters	alpha \beta \gamma \Gamma \phi \Phi \Psi\ \tau \Omega\	{TEX()} {\alpha\ \beta\ \gamma\ \Gamma\ \phi\ \Phi\ \Psi\ \tau\ \Omega} {TEX}
Blackboard bold	{x\in\mathbb{R}\sub\mathbb{C	{TEX()} {x\in\mathbb{R}\subset\mathbb{C}} {TEX}
boldface (vectors)	mathbf{x}\cdot\mathbf{y} = 0\	{TEX()} {\mathbf{x}\cdot\mathbf{y} = 0} {TEX}
boldface (greek)	{boldsymbol{\alpha} + \boldsymbol{\beta} + \boldsymbol{\gamma\	{TEX()} {\boldsymbol{\alpha} + \boldsymbol{\beta} + \boldsymbol{\gamma}} {TEX}
Fraktur typeface	{mathfrak{a} \mathfrak{B\	{TEX()} {\mathfrak{a} \mathfrak{B}} {TEX}
Script	{mathcal{ABC\	{TEX()} {\mathcal{ABC}} {TEX}
Hebrew	aleph \beth \gimel \daleth\	{TEX()} {\aleph\ \beth\ \gimel\ \daleth} {TEX}
non-italicised characters	{mbox{abc\	{TEX()} {\mbox{abc}} {TEX}	{TEX()} {\mbox{abc} \,\!} {TEX}
mixed italics (bad)	{mbox{if} n \mbox{is even\	{TEX()} {\mbox{if} n \mbox{is even}} {TEX}	{TEX()} {\mbox{if} n \mbox{is even} \,\!} {TEX}
mixed italics (good)	{mbox{if }n\mbox{ is even\	{TEX()} {\mbox{if }n\mbox{ is even}} {TEX}	{TEX()} {\mbox{if }n\mbox{ is even} \,\!} {TEX}

!Parenthesizing big expressions

Feature	Syntax	How it looks rendered
Not good	( \frac{1}{2} )	{TEX()} {( \frac{1}{2} )} {TEX}
Better	left ( \frac{1}{2} \right )\	{TEX()} {\left ( \frac{1}{2} \right )} {TEX}

You can use various delimiters with \left and \right:

Feature	Syntax	How it looks rendered
Parentheses	left ( A \right )\	{TEX()} {\left ( A \right )} {TEX}
Brackets	~np~left [ A \right ]\~/np~	{TEX()} {\left [ A \right ]} {TEX}
Braces	{\left \{ A \right \	{TEX()} {\left \{ A \right \}} {TEX}
Angle brackets	left \langle A \right \rangle\	{TEX()} {\left \langle A \right \rangle} {TEX}
Bars and double bars	|\left | A \right | and \left \| B \right \	{TEX()} {\left | A \right | and \left \| B \right \|} {TEX}
Delimiters can be mixed, as long as \left and \right match	(left [ 0,1 \right\ |left \langle \psi \right\	{TEX()} {\left [ 0,1 \right ) $\backslash left\; \backslash langle\; \backslash psi\; \backslash right\; |\}\; \{TEX\}$
Use \left. and \right. if you don't want a delimiter to appear:	left . \frac{A}{B} \right \} \to X\	{TEX()} {\left . \frac{A}{B} \right \} \to X} {TEX}