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Explain what programs (based around LaTeX) I need to download (Windows) in order to write up a mathematical document (must be able to do basic things like type mathematical symbols, insert equation labels, make changes to font colours and sizes etc.)
There are many variants of programs, which I am confused about. If possible, explain each one: LaTeX, MiKTeX, TexMaker, TeXworks, LyX etc.
The following might be incorrect, imprecise and plain false:
LaTeX A collection of macros (format) of/for TeX. It is the most used format out there.
MiKTeX A LaTeX distribution (meaning a collection of packages) used on Windows PCs.
Texmaker An editor specifically made for TeX and friends. It has some nice features to help people write there stuff
TeXworks See Texmaker
LyX An editor which hides much of LaTeX from the user. Think of it as LaTeX for Word-people.
Google A handy search engine to look up stuff. All of the above could be easily found by a minute search (and most likely would be more precise and correct). If you like another more you might use this one.
Welcome to TeX.SE! TeX is the base of all the related (with it) typesetting systems. LaTeX is the first TeX based system with easier syntax from TeX. XeLaTeX is like TeX but supports almost any font too (LaTeX supports only some specific fonts). MiKTeX and LyX (Edit:) are not some other typesetting languages (See @CarLaTeX's comments) that I am not familiar but you can take a look here: What is MikTeX? and here: What is the difference between LyX and LaTeX?.
Also for the installation on windows here is the answer: How do I install TeX/LaTeX on Windows .
TeXWorks and TeXMaker are just editors with LaTeX support and not typesetting systems. Look here for editors: LaTeX Editors/IDEs.
I would made a comment than an answer but in order to help you I had to write an answer.
