Chapter 1 Introduction

Chapter 2 Elements of the theory of Picard-Lefschetz

Chapter 3 The topology of the non-singular level set and the variation operator of a singularity

Chapter 4 The bifurcation sets and the monodromy group of a singularity

Chapter 5 The intersection matrices of singularities of functions of two variables

Chapter 6 The intersection forms of boundary singularities and the topology of complete intersections

Chapter 7 Discussion of results

Chapter 8 Elementary integrals and the resolution of singularities of the phase

Chapter 9 Asymptotics and Newton polyhedra

Chapter 10 The singular index, examples

Chapter 11 The simplest properties of the integrals

Chapter 12 Complex oscillatory integrals

Chapter 13 Integrals and differential equations

Chapter 14 The coefficients of series expansions of integrals, the weight and Hodge filtrations and the spectrum of a critical point

Chapter 15 The mixed Hodge structure of an isolated critical point of a holomorphic function

Chapter 16 The period map and the intersection form