amsmath: better equation environments (e.g. align), matrices, etc.
amssymb: Quantity symbols, arrows, etc.
amstext: Additional mathematical writings
Conveniently, you can also express all packages in a single command.
\usepackage{amsmath,amssymb,amstext}
Basic elements
There are many basic elements, such as mathematical symbols, equations, powers, indices, Greek alphabet, etc. The dollar sign stands for a line-internal mathematical environment.
$\pm$ und $\mp$ % Plus-minus / minus-plus sign
$\cdot$ $\cdots$ $\ldots$ % Points
$\vdots$ $\ddots$ % Further points
$\leq$ / $\geq$ und $\neq$ % smaller than / larger than equal to and not equal to
$\cup$ $\cap$ $\in$ $\notin$ % Quantity symbols
% Equations with powers and indices
\begin{equation} % if equation* is omitted, the automatic numbering of equations is omitted
a^{2} + b^{2} = c^{2}
\end{equation}
\begin{equation}
\begin{aligned}
f(x) &= a_{0} + xb_{0} \\
f'(x) &= b_{0}
\end{aligned}
\end{equation}
% Accents, etc.
$\bar{v}$ $\vec{v}$ $\overline{vvv}$ % Accents
$\overbrace{abc}\underbrace{def}$ % Braces
Greek alphabet
Many capital letters do not have their own command because they look identical in Latin (e.g. Alpha, Beta, Epsilon). These are simply written as normal capital letters, not as \Alpha. Note: The tilde is used to ensure that there are spaces between the letters in the final document. The following serves as a template for copying!
Normal brackets () and square brackets [] do not require a command (cf. curved brackets, which require a backslash in front of them). In the case of fractions, for example, the brackets become larger. This is where the commands \left( and \right) are used, which work with all types of brackets.
\begin{equation}
\begin{aligned}
(a + b) &= [a + b] = \{a + b\} \\ % Curly brackets require a backslash
\left(\frac{a}{b}\right) &= \left[\frac{a}{b}\right]
\end{aligned}
\end{equation}
Arrows
There are many variations of arrows in all relevant directions. Note: The tilde is used to ensure that there are spaces between the letters in the final document. The following serves as a copy template!
$\leftarrow~\rightarrow~\longleftarrow~\longrightarrow~\leftrightarrow~\longleftrightarrow~
\uparrow~\downarrow~\updownarrow$ \\ \\
% The upper arrows as double arrows
$\Leftarrow~\Rightarrow~\Longleftarrow~\Longrightarrow~\Leftrightarrow~\Longleftrightarrow~
\Uparrow~\Downarrow~\Updownarrow$ \\ \\
% Slanted arrows that do not appear twice
$\nearrow~\searrow~\nwarrow~\swarrow$
Operators
Operators such as sum symbols, integral symbols, etc. also have specific commands.
\begin{equation}
\begin{aligned}
\sum_{k = 1}^{n} k &= \frac{n(n-1)}{2} \\ % Summation sign
\prod_{k = 1}^{n} k &= n! \\ % Product mark
\lim_{x \to \infty} f(x) &= \frac{1}{x^{2}} \\ % Limit value
\int_{a}^{b} f(x) &= F(x) % Integral sign
\end{aligned}
\end{equation}
Matrices
The structure of the matrices is the same. However, they may differ in the type of brackets, resulting in different letters, as can be seen below:
\begin{equation}
\begin{matrix} % without brackets
a & b \\
c & d
\end{matrix}
\end{equation}
\begin{equation}
\begin{pmatrix} % curly bracket
a & b \\
c & d
\end{pmatrix}
\end{equation}
\begin{equation}
\begin{bmatrix} % square bracket
a & b \\
c & d
\end{bmatrix}
\end{equation}
\begin{equation}
\begin{Bmatrix} % curly bracket
a & b \\
c & d
\end{Bmatrix}
\end{equation}
\begin{equation}
\begin{vmatrix} % straight bracket
a & b \\
c & d
\end{vmatrix}
\end{equation}
\begin{equation}
\begin{Vmatrix} % straight double bracket
a & b \\
c & d
\end{Vmatrix}
\end{equation}