Covering over two centuries of innovations in many of the central geometrical disciplines, Introduction to Topology and Geometry is the most comprehensive introductory-level presentation of modern geometry currently available.Unique in both style and scope, the book covers an unparalleled range of topics, yet strikes a welcome balance between academic rigor and accessibility. By including subject matter previously relegated to higher-level graduate courses in mathematics and making it both interesting and accessible, the author presents a complete and cohesive picture of the science for students just entering the field. Historical notes throughout provide readers with a feel for how mathematical disciplines and theorems come into being.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 Using a variety of theorems to tie these seemingly disparate topics together, the author demonstrates the essential unity of mathematics.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.