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biblio.tex
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There are several books covering some, most, all, or much more of the course material.
\begin{itemize}
\item Baez, Muniain, \textit{Gauge Fields, Knots and Gravity}, World Scientific 1994
\item Choquet-Bruhat, DeWitt-Morette, \textit{Analysis, manifolds, and physics, Part I: Basics (Revised edition)}, North-Holland 1982
\item Choquet-Bruhat, DeWitt-Morette, \textit{Analysis, manifolds, and physics, Part II (Revised and enlarged edition)}, North-Holland 2000
\item Fecko, \textit{Differential geometry and Lie groups for physicists}, Cambridge University Press 2006
\item Frankel, \textit{The Geometry of Physics: An Introduction} (Third edition), Cambridge University Press 2011
\item Hamilton, \textit{Mathematical Gauge Theory: With Applications to the Standard Model of Particle Physics}, Springer 2017\\
(preliminary version \url{http://www.mathematik.uni-muenchen.de/~hamilton/gaugetheory.php})
\item Hassani, \textit{Mathematical Physics: A Modern Introduction to Its Foundations (Second edition)}, Springer 2013
\item Lam, \textit{Topics in Contemporary Mathematical Physics (Second edition)}, World Scientific 2015
\item Naber, \textit{Topology, Geometry and Gauge Fields: Foundations (Second edition)}, Springer 2010
\item Nakahara, \textit{Geometry, Topology and Physics (Second edition)}, Institute of Physics Publishing 2003
\item Rudolph, Schmidt, \textit{Differential Geometry and Mathematical Physics: Part I. Manifolds, Lie Groups and Hamiltonian Systems}, Springer 2012
\item Rudolph, Schmidt, \textit{Differential Geometry and Mathematical Physics: Part II. Fibre Bundles, Topology and Gauge Fields}, Springer 2017
\item Schutz, \textit{Geometrical Methods of Mathematical Physics}, Cambridge University Press 1980
\item Szekeres, \textit{A Course in Modern Mathematical Physics: Groups, Hilbert Space and Differential Geometry}, Cambridge University Press 2004
\item Westenholz, \textit{Differential Forms in Mathematical Physics} (Revised edition), North Holland 1978
\end{itemize}
\noindent Topic-specific references follow.
\subsection*{Logic}
\begin{itemize}
\item Chiswell, Wilfrid, \textit{Mathematical Logic}, Oxford University Press 2007
\item Hammack, \textit{Book of Proof}, Virginia Commonwealth University\\
\url{http://www.people.vcu.edu/~rhammack/BookOfProof/}
\item Mendelson, \textit{Introduction to Mathematical Logic}, CRC Press 2015
\end{itemize}
\subsection*{Set theory}
\begin{itemize}
\item Adamson, \textit{A Set Theory Workbook}, Birkh\"auser 1997
\item Smullyan, Fitting, \textit{Set theory and the continuum problem}, Oxford University Press 1996
\item Takeuti, Zaring, \textit{Introduction to Axiomatic Set Theory}, Springer 1981
\end{itemize}
\subsection*{Topology}
\begin{itemize}
\item Adamson, \textit{A General Topology Workbook}, Birkh\"auser 1995
\item Kalajdzievski, \textit{An Illustrated Introduction to Topology and Homotopy}, CRC Press 2015
\item Munkres, \textit{Topology} (Second edition), Pearson 2014
\end{itemize}
\subsection*{Topological manifolds}
\begin{itemize}
\item Lee, \textit{Introduction to Topological Manifolds} (Second edition), Springer 2011
\end{itemize}
\subsection*{Linear algebra}
\begin{itemize}
\item J\"anich, \textit{Linear algebra}, Springer 1994
\item Lang, \textit{Linear Algebra} (Third edition), Springer 1987
\item Shakarchi, \textit{Solutions Manual for Lang's Linear Algebra}, Springer 1996
\end{itemize}
\subsection*{Differentiable manifolds}
\begin{itemize}
\item Gadea, Masqu\'e, Mykytyuk, \textit{Analysis and Algebra on Differentiable Manifolds: A Workbook for Students and Teachers (Second Edition)}, Springer 2013
\item J\"anich, \textit{Vector Analysis}, Springer 2001
\item Lang, \textit{Fundamentals of Differential Geometry}, Springer 1999
\item Lee, \textit{Introduction to Smooth Manifolds} (Second edition), Springer 2012
\item Warner, \textit{Foundations of Differentiable Manifolds and Lie Groups}, Springer 1983
\end{itemize}
\subsection*{Lie groups and Lie algebras}
\begin{itemize}
\item Das, Okubo, \textit{Lie Groups and Lie Algebras for Physicists}, World Scientific 2014
\item Erdmann, Wildon, \textit{Introduction to Lie Algebras}, Springer 2006
\item Hall, \textit{Lie Groups, Lie Algebras, and Representations: An Elementary Introduction (Second edition)}, Springer 2015
\item Kirillov, \textit{An Introduction to Lie Groups and Lie Algebras}, Cambridge University Press 2008
\item Stillwell, \textit{Naive Lie Theory}, Springer 2008
\end{itemize}
\subsection*{Representation theory}
\begin{itemize}
\item Fuchs, Schweigert, \textit{Symmetries, Lie Algebras and Representations: A Graduate Course for Physicists}, Cambridge University Press 1997
\item Fulton, Harris, \textit{Representation Theory: A First Course}, Springer 2004
\item Zee, \textit{Group Theory in a Nutshell for Physicists}, Princeton University Press 2016
\end{itemize}
\subsection*{Principal bundles}
\begin{itemize}
\item Sontz, \textit{Principal Bundles: The Classical Case}, Springer 2015
\item Sontz, \textit{Principal Bundles: The Quantum Case}, Springer 2015
\end{itemize}