The goal is to give a comprehensible introduction into the topics and methods of modern condensed
matter theory. The course consists of two parts. The first one starts with an instruction on the
nowadays `traditional´ diagrammatic technique supplemented by a detailed survey of the problems
which are solved using this method, including Landau's theory of quantum liquids and BCS
theory of superconductivity. The second part of the course deals with problems which require the use
of more advanced non-perturbative approaches such as renormalisation group transformations,
bosonization and Bethe Ansatz. These concepts will be introduced on the examples of quantum
impurity problems such as potential scattering in Luttinger liquids, interedge tunnelling in fractional
quantum Hall probes and Kondo effect in metals and mesoscopic quantum dots.
Introductory materials: bosons, fermions and second quantisation
Green‘s functions approach
Exactly solvable problems: potential scattering, Luttinger liquids etc.
Theory of quantum fluids, BCS theory of superconductivity
Quantum impurity problems: Kondo effect, Anderson model, renormalisation