Text Editors
nano
Probably the best option for people who do not have much experience in Linux, and using a terminal-based interface. Commands are similar to normal word processing applications.
gedit
A good option if a remote graphical display (X11) is available. Commands are similar to normal word processing applications.
vim
Powerful but very different from a typical word processing application. There are two modes of operation: moving mode, and editing mode. To move the cursor around the document, you have to be in move mode. To interactively change the document, you switch to edit mode. You can programmatically make changes, too. Say, "change all occurrences of the string 'foo' which occur at the start of the line to 'bar'". Or, "delete the next 4 words".
emacs
Very powerful and extensible. You can run an email app and even a web browsing app written as Emacs applications. Commands are also very different from a typical word processing application.
atom
Graphical text editor, which runs on multiple platforms including Linux, Windows, and macOS. Requires a remote X11 display.