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.