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.

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.

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.

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.

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.

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.

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.

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.