Cover -- Title Page -- Copyright Page -- Table of Contents -- Chapter 1. Introduction -- 1.1 Key notions and notation -- Chapter 2. Gâteaux Dfferentiability of Lipschitz Functions -- 2.1 Radon-Nikodým Property -- 2.2 Haar and Aronszajn-Gauss Null Sets -- 2.3 Existence Results for Gâteaux Derivatives -- 2.4 Mean Value Estimates -- Chapter 3. Smoothness, Convexity, Porosity, and Separable Determination -- 3.1 A criterion of Differentiability of Convex Functions -- 3.2 Fréchet Smooth and Nonsmooth Renormings -- 3.3 Fréchet Differentiability of Convex Functions -- 3.4 Porosity and Nondifferentiability -- 3.5 Sets of Fréchet Differentiability Points -- 3.6 Separable Determination -- Chapter 4. ε-Fréchet Differentiability -- 4.1 ε-Differentiability and Uniform Smoothness -- 4.2 Asymptotic Uniform Smoothness -- 4.3 ε-Fréchet Differentiability of Functions on Asymptotically Smooth Spaces -- Chapter 5. Γ-Null and Γn-Null Sets -- 5.1 Introduction -- 5.2 Γ-Null Sets and Gâteaux Differentiability -- 5.3 Spaces of Surfaces -- 5.4 Γ- and Γn-Null Sets of low Borel Classes -- 5.5 Equivalent Definitions of Γn-Null Sets -- 5.6 Separable Determination -- Chapter 6. Fréchet Differentiability Except for Γ-Null Sets -- 6.1 Introduction -- 6.2 Regular Points -- 6.3 A Criterion of Fréchet Differentiability -- 6.4 Fréchet Differentiability Except for Γ-Null Sets -- Chapter 7. Variational Principles -- 7.1 Introduction -- 7.2 Variational Principles via Games -- 7.3 Bimetric Variational Principles -- Chapter 8. Smoothness and Asymptotic Smoothness -- 8.1 Modulus of Smoothness -- 8.2 Smooth Bumps with Controlled Modulus -- Chapter 9. Preliminaries to Main Results -- 9.1 Notation, Linear Operators, Tensor Products -- 9.2 Derivatives and Regularity -- 9.3 Deformation of Surfaces Controlled by ωn -- 9.4 Divergence Theorem -- 9.5 Some Integral Estimates.

Chapter 10. Porosity, Γn- and Γ-Null Sets -- 10.1 Porous and σ-Porous Sets -- 10.2 A Criterion of Γn-nullness of Porous Sets -- 10.3 Directional Porosity and Γn-Nullness -- 10.4 σ-Porosity and Γn-Nullness -- 10.5 Γ1-Nullness of Porous Sets and Asplundness -- 10.6 Spaces in which σ-Porous Sets are Γ-Null -- Chapter 11. Porosity and ε-Fréchet Differentiability -- 11.1 Introduction -- 11.2 Finite Dimensional Approximation -- 11.3 Slices and ε-Differentiability -- Chapter 12. Fréchet Differentiability of Real-Valued Functions -- 12.1 Introduction and Main Results -- 12.2 An Illustrative Special Case -- 12.3 A Mean Value Estimate -- 12.4 Proof of Theorems -- 12.5 Generalizations and Extensions -- Chapter 13. Fréchet Differentiability of Vector-Valued Functions -- 13.1 Main Results -- 13.2 Regularity Parameter -- 13.3 Reduction to a Special Case -- 13.4 Regular Fréchet Differentiability -- 13.5 Fréchet Differentiability -- 13.6 Simpler Special Cases -- Chapter 14. Unavoidable Porous Sets and Nondifferentiable Maps -- 14.1 Introduction and Main Results -- 14.2 An Unavoidable Porous Set in ℓ1 -- 14.3 Preliminaries to Proofs of Main Results -- 14.4 The Main Construction -- 14.5 The Main Construction -- 14.6 Proof of Theorem -- 14.7 Proof of Theorem -- Chapter 15. Asymptotic Fréchet Differentiability -- 15.1 Introduction -- 15.2 Auxiliary and Finite Dimensional Lemmas -- 15.3 The Algorithm -- 15.4 Regularity of f at x∞ -- 15.5 Linear Approximation of f at x∞ -- 15.6 Proof of Theorem -- Chapter 16. Differentiability of Lipschitz Maps on Hilbert Spaces -- 16.1 Introduction -- 16.2 Preliminaries -- 16.3 The Algorithm -- 16.4 Proof of Theorem -- 16.5 Proof of Lemma -- Bibliography -- Index -- Index of Notation.