Elementary Differential Topology
Review Of Calculus Of Several Variables and Linear Algebra Curves And Isoperimetric Inequality, Surfaces, Gauss Map, Principle Curvatures And Gauss Bonnet Theorem, A Visit To Hyperbolic Geometry.

References:
Calculus on Manifolds by M Spivak

Topology
Review of Point set Topology, quotient topology, compactness, connectedness, Simplicial Homology Theory, Brower’s Fixed Point Theorem, Leftschetz Fixed Point Theorem, Borsuk-Ulam Theorem

References:
1. Basic Topology by Armstrong.
2. Algebraic Topology, a Primer by S Deo.

Topology
Fundamental Groups and Covering Spaces: Examples, Lifting Path Homotopies, covering transformation, connection between fundamental group and covering spaces, universal covering space, Van Kampen Theorem.

References:
Algebraic Topology,M J Greenberg

Differential Topology
Smooth (abstract) manifolds, Tangent and cotangent bundles, Submersions, Immersions, Embeddings, Submanifolds, Regular and critical values, and Sard’s theorem.

References:
1. Introduction to Smooth Manifolds by J.M. Lee.
2. Elements of Differential Topology by A.R. Shastri.
3. Topology from the Differentiable view point by J. Milnor.
4. Differential Topology by Guillemin and Pollack.