%Anything following a percent symbol is a comment

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\documentclass[10pt]{article}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}

%This is where the document begins
\begin{document}
    
    %Creates bulleted statements following the \item declaration
  \begin{itemize}
        
    %First bullet
    \item \LaTeX \space is great for creating mathematical documents.
    
    %Next bullet
    \item Here are a few preliminaries:
     \begin{itemize}
      \item There are 10 special characters used only in \LaTeX \space commands.\\
       These are \begin{verbatim} # $ % & ~ ^ \ _ { } \end{verbatim} In order to have them appear 
in your document, you must use the begin-end verbatim block. You can also use a backslash to escape 
the meaning. For example a backslash followed by a dollar sign prints the \$ in your document.
                
      \item A backslash before a word such as \begin{verbatim} \begin{enumerate} \end{verbatim} is a 
declaration and produces the environment you want to work in (with the exception of escaping special 
characters). To close the block after you've added all your content, use the declaration
       \begin{verbatim} \end{enumerate} \end{verbatim}
                
       \item The 10 special characters above have different meanings in \LaTeX. Anything following \% 
is a comment and won't be printed in the final typeset document. Most important for mathematics is 
the \$\$. The the two dollar signs gives you the math environment. It is between these two symbols 
that you enter formulae. A double dollar sign will center your formula on the next line. 
\$\$ \em{formula here} \$\$.
                
     \end{itemize}
        
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      \item Here are a few examples of common mathematical things that \LaTeX \space can do:
       
       %Enumerates statements following the \item declaration.
       \begin{enumerate}
                
        %First item in the list
        \item Matrices:
        
         %Creates an array
         \[ \left[ \begin{array}{ccc} 
           %items in the array
            \frac{\partial y_{1}}{\partial x_{1}} 
			  & \cdots & \frac{\partial y_{1}}{\partial x_{n}} \\
            \vdots & \ddots & \vdots \\
            \frac{\partial y_{m}}{\partial x_{1}} 
              & \cdots & \frac{\partial y_{m}}{\partial x_{n}}
             \end{array} \right]
         \]
                    
        %Next item in the enumerated list
        \item Theorems/Axioms etc...:\\
         
         %Theorem Environment
         \newtheorem{guess}{Theorem} 
         \newtheorem{axiom}{Axiom}   
                 
         
             \begin{guess}
                     This is theorem 1.
             \end{guess}
             \begin{guess}
                     This is theorem 2.
             \end{guess}
         
             \begin{axiom}
                     This is axiom 1.
             \end{axiom}
             \begin{axiom}
                     This is axiom 2.
             \end{axiom}
         
         \newtheorem{conjecture}{Conjecture}
             \begin{conjecture}
                 Wikibooks has more information on options!
             \end{conjecture}
             
        %Pagebreak
        \clearpage
        
        %Next item      
        \item Equation Arrays:\\
        
         Numbered equations:
         \begin{eqnarray}
             ax^2 + bx + c & = & 0\\
             x & = & \frac{-b \pm \sqrt{b^2-4ac}}{2a}
         \end{eqnarray}
         
         Or unumbered equations:
         
         \begin{eqnarray*}
             ax^2 + bx + c & = & 0\\
             x & = & \frac{-b \pm \sqrt{b^2-4ac}}{2a}
         \end{eqnarray*}
        
        %Next item
        \item Tables:\\
         Lets create a table of values for the following parametric equations:
         
         \begin{eqnarray*}
             x & = & t^2 - 4 \\
             y & = & \frac{t}{2}
         \end{eqnarray*}
         
         %Here's the table
         \begin{center}
             
         \begin{tabular}{|c|c|c|}                            \hline
             t       &   x       &   y                   \\  \hline\hline
             $-2$    &   0       &   $-1$                \\  \hline
             $-1$    &   $-3$    &   $-\frac{1}{2}$      \\  \hline
             0       &   $-4$    &   0       \\  \hline
             2       &   0       &   1       \\  \hline
         \end{tabular}
                
            \end{center}
                
        %Simple pictures
        \item Picture environment\\
        Here is an example of how to use the picture environment to draw a right triangle.\\
        
         \setlength{\unitlength}{.4in}           
         \begin{picture}(7,5)(0,0)
          \linethickness{1pt}
          \put(0,0){\line(1,0){4}}
          \put(4,0){\line(0,1){3}}
          \put(0,0){\line(4,3){4}}
          \put(2,-.25){\makebox(0,0){$\alpha$}}
          \put(4.25,1.5){\makebox(0,0){$\beta$}}
          \put(2,2){\makebox(0,0){$\gamma$}}
         \end{picture}
         
         
         
       \end{enumerate}
  \end{itemize}
\end{document}