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Gnu Emacs is a highly customizable, Open Source, editing environment. Newbies tend to find it little more frightening to configure than its common alternative, Vim. Though once mastered, Emacs' built-in extension language is highly flexible, offering unlimited modification.
The current version, as of April 2014, is Emacs 24.3.
Due to the nature of Linux, users are often times at the discretion of their distribution package managers. As such, to install the latest offered version use your corresponding install command, in example:
Debian based (including Ubuntu/Mint)
sudo apt-get install emacs
Red Hat (Fedora)
sudo yum install emacs
sudo pacman -Sy emacs
If you are using a Debian-based or Red Hat-based distribution, I recommend finding an alternative package source to ensure the latest version. You will want Emacs 24+ to use the internal package manager.
Emacs binaries for the Mac can be acquired and installed from http://emacsformacosx.com/.
Emacs binaries for Windows can be acquired from http://ftp.gnu.org/gnu/emacs/windows/. These are in a zip file and can be ran locally. It is recommended you add the path you unzip in to your Environment Path.
Coming from other editors and just want to get going? Use a pre-built package such as Batsov's excellent Prelude. It is an all inclusive pack to make Emacs behave very similar to a full featured IDE.