% 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}