Algebraic topology: Fundamental group

This lecture is part of an online course on algebraic topology. We define the fundamental group, calculate it for some easy examples (vector spaces and spheres), and give a couple of applications (R^2 is not homeomorphic to R^3, the Brouwer fixedpoint theorem). For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj52yxQGxQoxwOtjIEtxE2BWx