A continuation on the fundamental group of a surface, we prove that the multiplication of equivalence classes or types of loops from a base point does indeed form a group in the algebraic sense. We discuss the fundamental group of the torus and the projective plane.This is part of a beginner's course on Algebraic Topology, given by N J Wildberger of UNSW.NOTE: This entire series is now available in the full (hour long lectures), also at this channel under the playlist AlgTop (full lectures):http://www.youtube.com/playlist?list=PL6763F57A61FE6FE8&feature=view_all
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