  In this expository introductory text we discuss the multiplier ideals in
algebraic geometry. We state Kawamata-Viehweg's and Nadel's vanishing theorems,
give a proof (following Ein and Lazarsfeld) of Koll\'ar's bound on the maximal
multiplicity of the theta divisor, and explain the asymptotic constructions and
the ideas of Siu's proof of the deformation invariance of plurigenera. We also
indicate the analytic interpretation of the theory.
