The aim of the course is to build a bridge between the physics of many-body interacting systems in condensed matter and quantum field theory. Several topics will be discussed, including

• the polaron problem
• the theory of interacting Fermi systems
• quantum electrodynamics of condensed matter.

As an addition, a number of many-particle problems that admit analytical solutions can be discussed: the system of weakly interacting bosons, the Bardeen-Cooper-Schrieffer model, the one-dimensional Bethe ansatz.