% This line can be ignored for our purposes.
\documentclass[10pt,a4paper]{article}

\begin{document}
% Everything below this line is considered as output of your document.

% Start a new section with the given headline.
\section{First Heading}

some text

% Start a new subsection with the given headline.
\subsection{Subheading}

some more text

\subsection{Another Subheading}

even more text

\section{Mathematical environments}

% The simple mathematical environment (math mode) is written in dollars.
The Pythagorean theorem says that $a^2 + b^2 = c^2$ holds for any right-angled triangle.

% The equation environment centers and activates math mode.
% Use equation* to suppress numbering on the right-hand side.
\begin{equation}
 \frac{3}{6} = \frac{1}{2}
\end{equation}

\end{document}