GIMP is the GNU Image Manipulation Program. It is a freely distributed piece of software for such tasks as photo retouching, image composition and image authoring. GIMP is a versatile graphics manipulation package and it works on Linux, Windows, Mac, OpenSolaris and FreeBSD. It is also available in many languages. The official GIMP Project website has a very good set of tutorials divided into the following levels: Beginner, Intermediate, Expert, Photo Editing, Web and Script Authoring.
If you prefer to take your reading away from the screen here are some book that can teach you a lot about this great image manipulation program.