Bases in Banach spaces: Schauder bases, Schur property, The Banach-Mazur Theorem and The Eberlein-
Smulian Theorem.

Classical Banach spaces and their properties: The Classical Sequence Spaces: The isomorphic structure of the lp -spaces and c0, Pitt’s Theorem, and complemented subspaces of lp and c0.

Banach Spaces of Continuous Functions: Basic properties, The Dunford-Pettis property and
characterization of real C(K)-spaces.

The Lp -spaces: The Haar system in Lp spaces (1 ≤ p < ∞) and Khintchine’s

M-ideals in Banach spaces: Definition and basic properties.