The composition of two symmetries (of an object or a physical theory) is again a symmetry. This gives a multiplication law on the symmetries which we call a group structure.
In this course you will learn to work with such group structures: we will start from finite groups to illustrate the basic definitions, but the main focus of this course lies on the Lie groups (continuous symmetries), especially for the unitary and rotation groups appearing in physics.
Apart from a few topological properties (compactness, connectedness, open and closed), we will also investigate the link between a Lie group and the associated Lie algebra (using the exponential map).
In a last part of the course, we will study 'representations' for Lie groups and algebras. Extra attention will obviously be paid to the spin representations for SU(2) and sl(2), and the representations for su(3) as these are related to quark models.