  These notes are based on a series of lectures given first at the University
of Warwick in spring 2008 and then at the Courant Institute, Imperial College
London, and EPFL. It is an attempt to give a reasonably self-contained
presentation of the basic theory of stochastic partial differential equations,
taking for granted basic measure theory, functional analysis and probability
theory, but nothing else.
  The approach taken in these notes is to focus on semilinear parabolic
problems driven by additive noise. These can be treated as stochastic evolution
equations in some infinite-dimensional Banach or Hilbert space that usually
have nice regularising properties and they already form a very rich class of
problems with many interesting properties. Furthermore, this class of problems
has the advantage of allowing to completely pass under silence many subtle
problems arising from stochastic integration in infinite-dimensional spaces.
