**[Cr:4, Lc:3, Tt:1, Lb:0]**

- Homotopy, retract, deformation retract, contractible spaces and homotopy type, fundamental group and its properties, The fundamental group of circle, van Kampen theorem (statement without proof), applications of van Kampen theorem.
- Simplicial complexes, polyhedra and triangulations, barycentric subdivision and simplicial approximation theorem.
- Orientation of simplicial complexes, simplicial chain complex and homology, properties of integral homology groups, induced homomorphisms. degree of a map from n-sphere to itself and its applications
- Invariance of simplicial homology groups. Lefschetz fixed point theorem, Borsuk-Ulam theorem.
- Definition and examples of covering spaces. path lifting and homotopy lifting property.
- Covering homomorphisms, deck transformations, classification of Coverings, existence of universal covering (statement without proof).
- Graphs, coverings of graphs and their fundamental groups.

- Satya Deo, Algebraic Topology: A Primer, Texts and Readings in Mathematics Vol. 27, Hindustan Book Agency (2003).
- William Massey, Algebraic Topology: An Introduction, Springer (Graduate Texts in Mathematice Vol. 127), (1977).
- Allen Hatcher, Algebraic Topology, Cambridge University Press (2002).
- M. Greenberg and J. Harper, Algebraic Topology: A First Course, Addision-Wesley (1981).
- H. Seifert and W. Threlfall, A Textbook of Topology, Academic Press (1980).