  This book is an introduction to the theory of stochastic partial differential
equations (SPDEs), using the random field approach pioneered by J.B. Walsh
(1986). The volume consists of two blocks: the core matter (Chapters 1 to 5)
and the appendices (A, B and C). Chapter 1 introduces the subject, with a
discussion of isonormal Gaussian processes, space-time white noise, and
motivating examples of SPDEs. Chapter 2 presents a theory of stochastic
integration with respect to space-time white noise. Chapter 3 deals with SPDEs
with additive noise. In Chapter 4, we study a general class of SPDEs, in which
additive and multiplicative nonlinearities appear. In Chapter 5, we present a
selection of important topics in the theory of SPDEs, that have been the
subject of much research over the last twenty years. Appendix A summarises the
main results from the theory of stochastic processes and stochastic analysis
that are used throughout the book. Appendix B is devoted to a systematic
presentation of properties of fundamental solutions and Green's functions
associated to the classical linear differential operators (heat, fractional
heat and wave operators). Appendix C is a toolbox section. Each chapter is
followed by a "Notes" section, which gives historically important references,
original sources and points towards other related important contributions.
