  The "principle of the fermionic projector" provides a new mathematical
framework for the formulation of physical theories and is a promising approach
for physics beyond the standard model. The book begins with a brief review of
relativity, relativistic quantum mechanics and classical gauge theories, with
the emphasis on the basic physical concepts and the mathematical foundations.
The external field problem and Klein's paradox are discussed and then resolved
by introducing the so-called fermionic projector, a global object in space-time
which generalizes the notion of the Dirac sea. The mathematical core of the
book is to give a precise definition of the fermionic projector and to employ
methods of hyperbolic differential equations for its detailed analysis. The
fermionic projector makes it possible to formulate a new type of variational
principles in space-time. The mathematical tools for the analysis of the
corresponding Euler-Lagrange equations are developed. A particular variational
principle is proposed which gives rise to an effective interaction showing many
similarities to the interactions of the standard model.
  The main chapters of the book are easily accessible for beginning graduate
students in mathematics or physics. Several appendices provide supplementary
material which will be useful to the experienced researcher.
