Recently, a friend of mine, who is also a mathematician, received a new laptop equipped with Ubuntu, a version of the Linux operating system based on Debian. He asked then about the best available free LaTeX editor under Linux. There is no canonical answer to this question. I like to use Emacs and sometimes vim (old Unix habits). Many other editors have a LaTeX plugin such as gedit, geany, jedit, etc. There is also a bunch of LaTeX specific editors such as texworks, latexila, texmaker, kile, etc. For people not so familiar with Unix, I suggest to try gummi (for people familiar with Apple Macs) or texstudio (for people familiar with Microsoft Windows). People familiar with Scientific Workplace or Scientific Word may try lyx. This software universe is evolving so rapidly that this post will become obsolete very soon.