The course will cover a selection from the following topics

• homotopy sets, homotopy groups and the Hurewicz theorem
• fibrations and cofibrations
• generalized homology theories and spectra
• bundles and classifying spaces
• characteristic classes
• low-dimensional topology
• geometric group theory
• spectral sequences and cohomology operations

Books that can be used for some of these topics include:

1. G. Bredon: Topology and geometry, Springer GTM 139,
2. T. tom Dieck: Algebraic topology, EMS 2008
3. P. May: A concise course in algebraic topology, Chicago Lecture Notes in Mathematics, UChicago Press 1999
4. J. Milnor, J.D. Sasheff: Characteristic classes, (AM-76) Princeton University Press
5. Allen Hatcher: Vector Bundles & K-theory, online book
   http://www.math.cornell.edu/~hatcher/VBKT/VBpage.html