Topics related to surfaces Euclidean, spherical and hyperbolic geometry, the fundamental group, universal covering surfaces and more.

Presents a number of topics related to surfaces, such as Euclidean, spherical and hyperbolic geometry, the fundamental group, universal covering surfaces, Riemannian manifolds, the Gauss-Bonnet Theorem, and the Riemann mapping theorem. It also includes some material only tangentially related to surfaces, such as the Cauchy Rigidity Theorem, the Dehn Dissection Theorem, and the Banach-Tarski Theorem. The goal is to present a tapestry of ideas in a clear and rigorous yet informal way.