\documentclass[12pt,a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage[czech]{babel}
\usepackage[T1]{fontenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\begin{document}
\begin{enumerate}
\item % prvni tri itemy jdou resit pomoci begin{gather} \nonumber end{gather}
\[
\sum_{
\begin{subarray}{l}
i<n \\ i\,\text{sudé}
\end{subarray}
}
x_i^2 
\]
\item 
\[
I_4=
\begin{pmatrix} 
1 & 0 & 0 & 0 \\ 
0 & 1 & 0 & 0 \\ 
0 & 0 & 1 & 0 \\ 
0 & 0 & 0 & 1 
\end{pmatrix}
\]
\item
\[
|x| = 
\begin{cases}
\phantom{-}x &x \geq 0\\
-x &x \leq 0\\
\end{cases}
\]
\item
\begin{multline}
a+b+c+d+e+f+b+c+d+e+f+b+c+d+e+f\\+b+c+d+e+f+b+c+d+e+f+i+j+k+l+m+n\nonumber
\end{multline}
\item
\begin{align*}
a+b     &= c+d\\
x       &= w+y+z\\[5pt]
m+n+o+p &=q
\end{align*}
\item
\begin{alignat*}{2}
a + b + c &+ d    & &= 0\\
        c &+ d + e& &= 5
\end{alignat*}
\item
\begin{alignat}{4}
a_{11}x_1	&+a_{12}x_2&	   {}&+a_{13}x_3&		  &&          &=y_1\\
a_{21}x_1	&+a_{22}x_2&		    &&             &+a_{24}x_4&	  &=y_2\notag\\
a_{31}x_1       &&          {}&+a_{33}x_3&	  &+a_{34}x_4&	  &=y_3
\end{alignat}
\item
\begin{align*}
&x_{1} + y_{1} + \left( \sum_{i < 5}
\binom{5}{i} + a^{2} \right)^{2}\\
&\phantom{x_{1} + y_{1} + {}}
\left( \sum_{i < 5} \binom{5}{i}
+ \alpha^{2} \right)^{2}
\end{align*}
\item
\[
\begin{aligned}
\alpha &= \alpha \alpha\\
\beta &= \beta\beta\beta\beta\beta\\
\gamma &= \gamma
\end{aligned}
\text{\qquad versus \qquad}
\begin{gathered}[t]
\delta = \delta\delta \\
\eta = \eta\eta\eta\eta\eta \\
\varphi = \varphi \\
\end{gathered}
\]
\item
\begin{align}
\begin{split}
a &= b+c-d\\
&=g+h\\
&=i\\
&=j
\end{split}
\end{align}
\end{enumerate}
\end{document}