Homotopy. Fundamental group. Examples and applications: fundamental group of the circle, projective spaces, classical groups. Seifert and Van Kampen’s theorem. Covering spaces. Covering and fundamental group. Universal covering. Fundamental group of compact surfaces. Double oriented covering. Other topics.

References:
FULTON, W. – Algebraic topology, Springer, 1999.
LIMA, E. L. – Fundamental Group and Recovering Spaces. Euclid Project. Rio de Janeiro, IMPA, 2006.
MASSEY, W. S. – A Basic Course in Algebraic Topology, Graduate Texts in Mathematics, Springer-Verlag, 1991.

* Basic syllabus. The teacher has the autonomy to make any changes.