The purpose of this page is to deal with the many packages that are available in LaTeX. And there are probably a lot I'm not even aware of at this time.
Let's begin with
\usepackage{amsfonts} -- an extended set of fonts.
\usepackage{amsmath} -- adds more math structures and operations.
\usepackage{amssymb} -- supersedes amsfonts.
\usepackage{dsfont} -- a set of blackboard bold fonts.
\usepackage{xy}. This link takes you to my page that describes how to create beautiful math diagrams.
\usepackage{mathrsfs} -- defines script style fonts.
\usepackage{multirow} -- 'Create tabular cells spanning multiple rows' (from the CTAN page).
\usepackage{bigstrut} -- used to produce an invisible strut that can help to vertically space entries or fractions.
\usepackage{relsize} -- used to resize text or msath by modifiers: \small, \normalsize, \large, \Large, \LARGE, \huge,...
\usepackage[utf8]{inputenc} -- for accents and ligatures, mainly with UTF8 encoding.
\usepackage{framed} -- draws boxes around objects for emphasis.
\usepackage{stmaryrd} -- provides an extended set of names to refer to math symbols not defined by standard LaTeX.
\usepackage{geometry} -- used to establish the page metrics of the document.
\usepackage{float} -- used to place a table in such a way as to facilitate nice-looking pagination of the text.
\usepackage{mathtools} -- provides many enhancemnts to amsmath, including a simplified math alignment environment.
\usepackage[shortlabels] -- generally for enumerate/enumitem environemnt.
\usepackage[normalem]{ulem} -- use to strike out text or for various kinds of underlining.
\usepackage{comment} -- provides a user commenting environment that is more convenient than using %s.
\usepackage{graphicx} -- a package to deal with graphics.
\usepackage{cancel} -- provides a command to strike out a character or math symbol.
\usepackage{gensymb} -- according to the CTAN page, 'Provides generic commands \degree, \celsius, \perthousand, \micro and \ohm which work both in text and maths mode'.
\usepackage[version=4]{mhchem} -- provides command to typeset for chemistry.
\usepackage{bigints} -- highly specialized for making big integral signs.
\usepackage{ctable} -- for multipage tables.
\usepackage{bbold} -- the so-called blackboard bold characters, much needed in mathematics for naming the common sets of numbers.
\usepackage{latexsym} -- an additional font package.