Module I (15 hours)
Categories, Functors, Natural transformations, natural equivalence, paths and path connected spaces, Affine spaces, Affine maps, Homotopy, Homotopy as equivalence relation, Contractible Spaces, Homotopically equivalent spaces with examples, Fundamental Groups, Induced maps and homomorphisms, Lifting property, Calculation of first homotopy groups, Seifert-van kampen theorem.

Module II (15 hours)
Group objects and cogroup objects, Loop space and suspension, Exact sequence of homotopy groups, Homotopy extension property, Fibrations and cofibrations, CW-complexes and their examples, attaching of maps, Homotopy groups of CW-complexes, The effect on the homotopy groups of a cellular extension, Spaces with prescribed homotopy groups, Weak homotopy equivalences and CW-approximation, Homotopy extension and classification theorems.

To give an idea of transforming topological problems into algebraic one.

To introduce the applications of topology.

CO1. Students will have knowledge of algebraic invariants such as fundamental groups used in algebraic topology.

CO2. They will learn about covering space theory and its application to fundamental groups.

CO3. Students will be able to compute fundamental groups by using the Seifert-Van Kampen Theorem.

CO4. Students will learn to apply the concepts of category theory to topology.

CO5. They will learn about CW-complexes and their homotopy groups.

J. J. Rotman, An Introduction to Algebraic Topology, Springer-Verlag

E. H. Spanier, Algebraic Topology, McGraw Hill

W. S. Massey, Algebraic Topology-An Introduction, Springer-Verlag

G. E. Bredon, Topology and Geometry, Springer-Verlag