The course gives an up-to-date and modern overview of the main concepts in Group Theory. Group theoretical properties and several examples of groups arising in many branches of mathematics, physics, and chemistry are studied to show how group theory emerges in different mathematical fields and in applied sciences.

This course aims to introduce students to classical and quantum mechanics by means of a mathematically rigorous approach. In the first part of the course we shortly introduce Newtonian mechanics and develop Lagrangian and Hamiltonian mechanics on manifolds with a particular emphasis on the underlying variational principles.  The second part introduces Quantum Mechanics in an axiomatic way and is focused on the study of  the spectral properties of the Schrödinger Hamiltonian for different classes of potentials.