1. Point Set Topology: Open and Closed Sets, Bases and Subbases, Nets and Subnets, Separability, Axioms of Countability. Metrizability. Compactness.
2. Topological Vector Spaces: Convex and Balanced Sets. Locally Convex Spaces. Normable spaces. Metrizable spaces.
3. Weak and Weak* Topologies: Sequences. Continuous Functions. Separability. Duality. Convex and Balanced Sets. Metrizability. Goldstine's Theorem. Alaglu's Theorem. The Eberlein-Smulian Theorem.