A sweeping yet uniquely accessible introduction to a variety of central geometrical topics Students and teachers will benefit from a uniquely unified treatment of such topics as: Homeomorphism Graph theory Surface topology Knot theory Differential geometry Riemannian geometry Hyperbolic geometry Algebraic topology General topology A logical yet flexible organization makes the text useful for courses in basic geometry as well as those with a more topological focus, while exercises ranging from the routine to the challenging make the material accessible at varying levels of study.