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Geometry Geometry: Plane and Fancy (Undergraduate Texts in Mathematics) by David A. Singer
. This is a book on non-Euclidean geometry aimed at those who have studied algebra and geometry at the high school level. In the process of examining geometric objects, the author incorporates some graph theory, some topology, and the algebra of complex (and hypercomplex) numbers. Although many concepts introduced are advanced, the mathematical techniques are not. The concepts learned here can be reapplied when learning about curved spacetime later. Buy this book

Taxicab Geometry: An Adventure in Non-Euclidean Geometry by Eugene F. Krause
. Simple non-Euclidean geometry describes curved space, and hence this topic provides an easy way to learn techniques for later dealing with curved spacetime in general relativity. This book develops a simple non-Euclidean geometry and explores some of its practical applications through graphs, research problems, and exercises. Buy this book

Geometrical Methods of Mathematical Physics Geometrical Methods of Mathematical Physics by Bernard F. Schutz
. Written at a level appropriate for graduate students and advanced undergraduates in the fields of relativity and cosmology, high-energy physics and field theory, thermodynamics, fluid dynamics and mechanics, this book provides an introduction to the concepts and techniques of modern differential theory, particularly Lie groups, Lie forms and differential forms. I learned a lot from it myself, despite all the fancier books that I have read. Buy this book

The Geometry of Physics : An Introduction by Theodore Frankel
. This new book provides a working knowledge of exterior forms and differential geometry. It also gives readers a view of selected topics in algebraic and differential topology, Lie groups and vector bundles, together with applications to Hamiltonian mechanics, fluid mechanics, elasticity, electromagnetism in flat and curved space, thermodynamics, general relativity, the Dirac equation, and gauge theories. Buy this book

Geometry, Topology and Physics Geometry, Topology and Physics (Graduate Student Series in Physics) by M. Nakahara
. This is a good textbook for physics graduate students who want to learn homotopy, homology, cohomology, or other areas of differential geometry and topology that are useful in physics. It covers a bit of string theory in a section on the Polyakov action. The clarity of the presentation is enhanced by explicit calculations and diagrams; the proof of a theorem is given only when it is instructive and not very technical. Buy this book

Group Theory in Physics: An Introduction by J. F. Cronwell (Editor), J. F. Cornwell (Editor)
Group Theory in Physics - An Introduction is an abridgement and revision of Volumes I and II of the author's previous three volume work Group Theory in Physics. It has been designed to provide a succinct introduction to the subject for advanced undergraduate and postgraduate students, and for others approaching the subject for the first time. Buy this book

Mathematical Groups Mathematical Groups (Teach Yourself) by Tony Barnard, Hugh Neill (Contributor), Tim Barnard
. Here's a book on group theory specifically oriented towards the self-learner. In particle physics and string theory, a little understanding of group theory can go a long way. This book will help you get started. Buy this book


Group Theory in Physics by Wu-Ki. Tung
. An introductory text book for graduates and advanced undergraduates on group representation theory. It emphasizes group theory's role as the mathematical framework for describing symmetry properties of classical and quantum mechanical systems. Buy this book
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