Latex has a special mode for formatting mathematical formulas. Simply enclose code that you want to be rendered in mathmode in $s.
When in this mode it is possible to displaying complicated mathematical notations.
This mode allows the use of subscripts, superscripts, fractions, summations, integrals, Greek letters and many other notations & special symbols.
In order to load a package in LaTeX, simply type \usepackage{packagenamehere} in the preamble of your document, before the \begin{document} statement.
Used to typeset mathematical notation
Used to typeset theorems
An extended set of fonts and symbols
An extended set of fonts and symbols
mathtools
An extension of amsmath
tikz
A package for drawing graphics directly with LaTeX commands
Inkscape is commonly used for producing pictures, which can be included in a LaTeX document with e.g. the graphicx package. You can render LaTeX in your Inkscape pictures using Extensions->Render->LaTeX formula, and you can export as tikz-style code using the extension svg2tikz (at the time of writing the "Documentation" link is broken; an installation guide can be found here)
tikz-cd
A package for drawing commutative diagrams.
Quiver is a very useful graphical commutative diagram editor which can export tikz-cd-style code.
Not a package, but many journals require submissions to use the amsart documentclass, which you can use by including \documentclass{amsart} in your preamble. This documentclass is often considered more attractive than article documentclass, and automatically includes the amsmath and amsthm packages.