The study of Kurt Godel's proof of the "incompleteness" of a formal system such as "Principia Mathematica" is a great way to stimulate students' thinking and creative processes and interest in mathematics and its important developments. This article describes salient features of the proof together with ways to deal with potential difficulties for students. It recommends the study of the logical-skeletal structure before students attempt the proof itself. It describes how students can be introduced to the proof with a documentary highlighting its importance; two books for the "general reader", Nagel and Newman (2001) and Frantzen (2005) are evaluated and the best description of its logical core written in clear English is given. The author also suggests a prior discussion about paradoxes in mathematics with students, in particular the Richard paradox, the Liar's paradox--"This sentence is false,"--and Bertrand Russell's set-theoretical paradox in the theory of classes. (Contains 10 notes.)