In presenting a detailed study of the geometry and topology of numerous classes of "generic" singularities, Geometry of Topological Stability bridges the gap between algebraic calculations and continuity arguments to detail the necessary and sufficient conditions for a C (infinity) to be C0-stable. Throughout, the authors masterfully examine this important subject using results culled from a broad range of mathematical disciplines, including geometric topology, stratification theory, algebraic geometry, and commutative algebra. Packed with original research, much of which is presented here for the first time, the book will be welcomed by students and researchers interested in singularity theory and related areas.