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, elasticity theory, the geometry and topology of Kirchhoff’s electric circuit laws, 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 advanced undergraduate students of physics, engineering, and mathematics. It can be used as a course text of for self-study.
This second edition includes three new appendices, Appendix C, Symmetries, Quarks, and Meson Masses （which concludes with the famous Gell-Mann/Okubo mass formula）; Appendix D, Representations
and Hyperelastic Bodies; and Appendix E, Orbits and Morse-Bott Theory in Compact Lie Groups. Both Appendix C and D involve results from the theory of representations of compact Lie groups,
which are developed here. Appendix E delves deeper into the geometry and topology of compact Lie groups.
Theodore Frankel received his Ph.D.from the University of California，Berkeley.He is currently emeritus professor of mathematics at the University of California，San Diego.
