Algebraic Topology

Simplicial and singular homology. Homotopy invariance theorem. Excision formula. Mayer-Vietoris sequence. Cellular homology. Cohomology and the universal coefficients theorem. Products in homology and cohomology. Künneth formula. Poincaré duality. De Rham’s theorem. Additional topics: Introduction to homotopy theory. Characteristic classes.

References:
Hatcher, A. Algebraic Topology. Cambridge University Press, 2002.
Bott, R. and Tu, L. W. Differential Forms in Algebraic Topology. Grad. Texts in Math. 82, Springer-Verlag, New York-Berlin, 1982.
Bredon, G. Topology and Geometry. Grad. Texts in Math. 139, Springer-Verlag, New York, 1997.