MiKTeX (pronounced mick-tech) is an up-to-date implementation of TeX/LaTeX and related programs.
TeX is a typesetting system written by Donald Ervin Knuth who says that it is intended for the creation of beautiful books - and especially for books that contain a lot of mathematics.
It is very easy to install MiKTeX on Windows. The MiKTeX Setup Wizard guides you through the installation process. You don't have to be a computer expert.
On a Mac, you can use the Homebrew package manager to install MiKTeX.
A complete set of additions (programs, styles, fonts, …) are available to help you typeset your documents.
MiKTeX's integrated package manager installs missing components from the Internet, if required.
For example, the LaTeX directive
would trigger the installer, if the memoir package is not already installed.
This unique feature allows you to keep your computer clutter-free: only install packages you actually need.
The MiKTeX Update Wizard helps you to keep your MiKTeX system up-to-date by installing the latest package updates.
The TeX output viewer Yap allows for an optimized edit-compile-view cycle (if the TeX authoring system in use supports source specials).
The MiKTeX package repository is updated regularly.
MiKTeX is open source. You are welcome to redistribute MiKTeX under certain conditions.