The course aims to offer a broad perspective on theoretical methods for quantum many-body systems. We will discuss quantum many body methods like large-N theory, dynamical mean field etc and methods for out of equilibrium dissipative and driven quantum systems, alongside applications to specific physical examples in both condensed matter and quantum optics arenas.

The course is addressed to students in experimental and theoretical condensed matter physics and provides a theoretical introduction to a variety of important concepts used in this field.

New platforms for exploring quantum many-body physics include moire systems in van der Waals materials, terahertz metamaterials with ultrastrong light matter coupling, cold atoms in optical lattices with tunable geometry and ensembles of atoms or molecules with non-local interactions. This course will review concepts central to these systems.

The lecture covers the concepts of classical and quantum statistical physics. The discussion ranges from foundations to specific systems, including their formalisms and techniques, such as bosonic and fermionic gases, and magnetism. Phenomena, most notably phase transitions, are treated by methods such as exact solutions, mean-field approximations, and the renormalization group.

This course will review recent progress in realizing strongly correlated many-body systems with ultracold atoms. Both theory and experiments will be discussed with an emphasis on the connection between the physics of ultracold atoms and correlated electron systems. The course will explore unique features of ultracold atoms such as dynamical control of Hamiltonians and single atom resolution.

The first (longer) part of the course treats phenomenological thermodynamics. This comprises basic notions such as heat and entropy, as well as the laws of thermodynamics. The second (shorter) part of the course is devoted to classical statistical mechanics. It discusses basic notions such as statistical ensembles.