  Multiplier ideals, and the vanishing theorems they satisfy, have found many
applications in recent years. In the global setting they have been used to
study pluricanonical and other linear series on a projective variety. More
recently, they have led to the discovery of some surprising uniform results in
local algebra.
  The present notes aim to provide a gentle introduction to the
algebraically-oriented local side of the theory. They follow closely a short
course on multiplier ideals given in September 2002 at the Introductory
Workshop of the program in commutative algebra at MSRI.
