\documentclass{article}
% this is a comment
% put the usepackage command 
% before begin document
\usepackage{amsmath}
\usepackage{graphicx}


\begin{document}

Hello. Latex will not see 
line breaks or
spaces        between      words.
If I want a new line\\
I can use a special command\newline
to do it.

A new paragraph has a blank row before it.

\section{Method}

In Section \ref{sec:Introduction}

\section{Results}

We can write maths inline like
this $a=bx$ using dollar signs.

If the maths is too big to fit on the line use a double dollar like this
$$
x= y^2 + z^2
$$
and we can carry on writing.

This equation has a full stop after
$$
x= y^2 + z^2.
$$

And we move to a new paragraph.

This equation will be referenced
later on in the document
\begin{equation}
x= y+z
\label{eqn:my first equation}
\end{equation}
Equation can only have one line.

Instead we can use the align environment.
\begin{align}
x=y+z \nonumber \\
+w+t
\end{align}

Now to do some more complex maths. We use underscore, overscore, and frac to develop an equation.
$$
A = \frac{x+\frac{1}{2}a + \frac{a+b}{c} }{y+x_iB^2}
$$

For an integral we use int
$$
I = \int_{y=x^2}^{\infty}\alpha x^2 dx
$$
For summations we have sum$$
A = \sum_{i=0}^N a_i \frac{1}{i!}
$$



\section{Introduction}
\label{sec:Introduction}

In equation 
(\ref{eqn:my first equation})
we show something.

We could put lines round everything
\begin{tabular}{|c|c|c|}
\hline
this is the first & second 
& third \\
\hline
1 & 2 & 3 \\
\hline
31 & 22 & 13 \\
\hline
1 & 2 & 3 \\
\hline
\end{tabular}

Or just a few lines
\begin{tabular}{c|cc}
this is the first & second 
& third \\
\hline
1 & 2 & 3 \\
31 & 22 & 13 \\
1 & 2 & 3 \\
\end{tabular}

The two examples above sit in the text. If we want the table to sit on its own use the table environment.
\begin{table}
\begin{center}
\begin{tabular}{c|cc}
this is the first & second 
& third \\
\hline
1 & 2 & 3 \\
31 & 22 & 13 \\
1 & 2 & 3 \\
\end{tabular}
\end{center}
\caption{A description of my table}
\end{table}


I need to put in another table, so I copy paste and then edit it.
\begin{table}
\begin{center}
\begin{tabular}{c|cccc}
this is the first & second 
& third \\
\hline
11 & 23& 344 & 23& 344 \\
31 & 242 & 153& 23& 344  \\
14 & 24 & 345& 23& 344  \\
\end{tabular}
\end{center}
\caption{A description of my table}
\end{table}

We can now include graphics with the command
\includegraphics{dog.jpg}
or put it on a new line\\
\includegraphics{dog.jpg}\\
will need blackslashes after the picture to start a new line.

To make a figure (a picture that can be referenced) use the figure environment.
\begin{figure}
\includegraphics{dog.jpg}
\caption{A picture of a dog.}
\label{fig:dog}
\end{figure}

\end{document}