\documentclass[12pt]{article}
\usepackage{amsmath}

\begin{document}

\section{Arrays}

\begin{equation}
A_1 = 
 \left( \begin{array}{rcl}1 & 2 & 3 \\
                        x^2 & 0 & \dfrac{y}{2x} \\
                          3 & x^2 + y^2 - z_0^2 & \sum_{n=0}^\infty x^{-an} \end{array} \right)
\end{equation}

\section{Counter Playing}

\newcounter{test}
\setcounter{test}{1}
First: \thetest.
\renewcommand{\thetest}{\Roman{test}}
Second: \thetest.
\renewcommand{\thetest}{\alph{test}}
Third: \thetest.
And some direct accesses: \arabic{test}, \roman{test}, \Alph{test}.

We repeat:
\renewcommand{\thetest}{\arabic{test}}
\addtocounter{test}{1}
First: \thetest.
\renewcommand{\thetest}{\Roman{test}}
Second: \thetest.
\renewcommand{\thetest}{\alph{test}}
Third: \thetest.
And some direct accesses: \arabic{test}, \roman{test}, \Alph{test}.

Some footnote characters:
\setcounter{test}{1}
\fnsymbol{test} \addtocounter{test}{1}
\fnsymbol{test} \addtocounter{test}{1}
\fnsymbol{test} \addtocounter{test}{1}
\fnsymbol{test} \addtocounter{test}{1}
\fnsymbol{test} \addtocounter{test}{1}
\fnsymbol{test} \addtocounter{test}{1}
\fnsymbol{test} \addtocounter{test}{1}
\fnsymbol{test} \addtocounter{test}{1}
\fnsymbol{test}

\LaTeXe

Enumerates:

\begin{enumerate}
\item test
  \begin{enumerate}
  \item test
    \begin{enumerate}
    \item test
      \begin{enumerate}
      \item test
      \item test
      \end{enumerate}
    \item test
    \end{enumerate}
  \item test
  \end{enumerate}
  \item test
\end{enumerate}

Itemize:

\begin{itemize}
\item test
  \begin{itemize}
  \item test
    \begin{itemize}
    \item test
      \begin{itemize}
      \item test
      \item test
      \end{itemize}
    \item test
    \end{itemize}
  \item test
  \end{itemize}
  \item test
\end{itemize}

  
\end{document}
