Quantum Theory of Fermion Systems:. Topics Between Physics and Mathematics

A pedagogical introduction to quantum models of fermions is given emphasizing the interplay between physics and mathematics. The aim is to explain physical ideas and mathematical tools by looking at simple examples. The topics discussed include fermion systems with a finite number of degrees of freedom, examples for the quantum field theory limit and regularization, the abstract formalism of quasi-free second quantization and some of its applications like the boson-fermion correspondence, loop algebras, and the Luttinger model.