Banach space theory: the basis for linear and nonlinear analysis

Basic concepts in Banach spaces

Hahn-Banach and Banach open mapping theorems

Weak topologies and Banach spaces

Schauder bases

Structure of Banach spaces

Finite-dimensional spaces

Optimization

C¹-smoothness in separable spaces

Superreflexive spaces

Higher order smoothness

Dentability and differentiability

Basics in nonlinear geometric analysis

Weakly compactly generated spaces

Topics in weak topologies on Banach spaces

Compact operators on Banach spaces

Tensor products

Appendix: Basics in topology

Nets and filters

Nets and filters in topological spaces

Ultraproducts

The order topology on the ordinals

Continuity of set-valued mappings

The cantor space

Baire's great theorem

Polish spaces

Uniform spaces

Nets and filters in uniform spaces

Partitions of unity

Measure and integral

Continued fractions and the representation of the irrational numbers.