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\title{\boldmath Lectures on the Geometric Anatomy\\of Theoretical Physics}


%% %simple case: 2 authors, same institution
\author{Dr Frederic P. Schuller} 
%\author{Simon Rea}
\affiliation{Friedrich-Alexander-Universit\"at Erlangen-N\"urnberg,\\Institut f\"ur Theoretische Physik III}

% more complex case: 4 authors, 3 institutions, 2 footnotes
%\author[a,b,1]{F. Irst,\note{Corresponding author.}}
%\author[c]{S. Econd,}
%\author[a,2]{T. Hird\note{Also at Some University.}}
%\author[a,2]{and Fourth}

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%\affiliation[a]{One University,\\some-street, Country}
%\affiliation[b]{Another University,\\different-address, Country}
%\affiliation[c]{A School for Advanced Studies,\\some-location, Country}

% e-mail addresses: one for each author, in the same order as the authors
\emailAdd{fps@aei.mpg.de}
%fschuller@perimeterinstitute.ca
%\emailAdd{second@asas.edu}
%\emailAdd{third@one.univ}
%\emailAdd{s.rea.hw@gmail.com}


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\begin{document} 

\rule{0cm}{2cm}\\
\includegraphics[width=14cm]{faulogo}
\maketitle


 \section*{Introduction}
 \addcontentsline{toc}{section}{Introduction}
 \markright{Introduction}
 \input{ga/00intro}
 \newpage

 \section{Logic of propositions and predicates}
 \input{ga/01logic}
 \newpage

 \section{Axioms of set theory}
 \input{ga/02axioms}
 \newpage

 \section{Classification of sets}
 \input{ga/03classification}
 \newpage

 \section{Topological spaces: construction and purpose}
 \input{ga/04topology}
 \newpage

 \section{Topological spaces: some heavily used invariants}
 \input{ga/05topology_inv}
 \newpage
 \section{Topological manifolds and bundles}
 \input{ga/06manifolds}
 \newpage

 \section{Differentiable structures: definition and classification}
 \input{ga/07differentiable}
 \newpage

 \section{Tensor space theory I: over a field}
 \input{ga/08tensor_i}
 \newpage

  \section{Differential structures: the pivotal concept of tangent vector spaces}
  \input{ga/09tangent_space}
  \newpage

 \section{Construction of the tangent bundle}
 \input{ga/10tangent_bundle}
 \newpage

 \section{Tensor space theory II: over a ring}
 \input{ga/11tensor_ii}
 \newpage

 \section{Grassmann algebra and de Rham cohomology}
 \input{ga/12grassmann}
 \newpage

 \section{Lie groups and their Lie algebras}
 \input{ga/13lie_groups}
 \newpage

 \section{Classification of Lie algebras and Dynkin diagrams}
 \input{ga/14classification}
 \newpage

 \section{The Lie group \texorpdfstring{$\SL(2,\C)$}{SL(2,C)} and its Lie algebra \texorpdfstring{$\sl(2,\C)$}{sl(2,C)}}
 \input{ga/15sl2}
 \newpage

 \section{Dynkin diagrams from Lie algebras, and vice versa}
 \input{ga/16dynkin}
 \newpage

 \section{Representation theory of Lie groups and Lie algebras}
 \input{ga/17representation}
 \newpage

 \section{Reconstruction of a Lie group from its algebra}
 \input{ga/18reconstruction}
 \newpage

 \section{Principal fibre bundles}
 \input{ga/19principal}
 \newpage

 \section{Associated fibre bundles}
 \input{ga/20associated}
 \newpage

 \section{Connections and connection 1-forms}
 \input{ga/21connections}
 \newpage

 \section{Local representations of a connection on the base manifold: Yang-Mills fields}
 \input{ga/22yang-mills}
 \newpage

 \section{Parallel transport}
 \input{ga/23parallel}
 \newpage

 \section{Curvature and torsion on principal bundles}
 \input{ga/24curvature}
 \newpage

 \section{Covariant derivatives}
 \input{ga/25covariant}
 \newpage

 \setcounter{section}{25}
 \section{Application: Quantum mechanics on curved spaces}
 \input{ga/26quantum}
 \newpage

 \section{Application: Spin structures}
 \input{ga/27spin}
 \newpage

 \section{Application: Kinematical and dynamical symmetries}
 \input{ga/28kinematical}
 \newpage

 \section*{Further readings}
 \addcontentsline{toc}{section}{Further readings}
 \input{biblio}

 \printindex

\end{document}