The geometry of physics : an introduction This book is intended to provide a working knowledge of those parts of exterior differential forms differential geometry algebraic and differential topology Lie groups vector bundles and Chern forms that are essential for a deeper understanding of both classical and modern physics and engineering. Included are discussions of analytical and fluid dynamics electromagnetism (in flat and curved space) thermodynamics the deformation tensors of elasticity soap films special and general relativity the Dirac operator and spinors and gauge fields including Yang Mills the Aharonov Bohm effect Berry phase and instanton winding numbers quarks and the quark model for mesons. Before a discussion of abstract notions of differential geometry geometric intuition is developed through a rather extensive introduction to the study of surfaces in ordinary space; consequently the book should be of interest also to mathematics students. This book will be useful to graduate and advance undergraduate students of physics engineering or mathematics. It can be used as a course text or for self study. This third edition includes a new overview of Cartans exterior differential forms. It previews many of the geometric concepts developed in the text and illustrates their applications to a single extended problem in engineering namely the Cauchy stresses created by a small twist of an elastic cylindrical rod about its axis