*Prerequisites*: Calculus, basics of set theory and group theory.

*Course description*: This course tries to give a quick insight to
various chapters of topology: the fundamental group, classification of
surfaces and knot theory. Rather than develop one part in great
detail, we will see a range of typical problems arising in topology,
and the different ways they can be answered. The theory will be
supported by many examples and excercises.

*Course outline:* the following topics will be covered (time permitting)

- A necessary but brief introduction to the basic notions of point-set topology (topological spaces, continuity, compactness, connectedness).
- The fundamental group: homotopies, covering spaces, applications to algebra and geometry.
- Classification of surfaces: examples of surfaces, orientation, Euler characteristic.
- Introduction to knot theory: the fundamental group of a knot, knot polynomials.