The School on Vanishing Theorems and Effective Results in Algebraic Geometry took place in ICTP, Trieste from 25 April 2000 to 12 May 2000. It was organized by J. P. Demailly (Université de Grenoble I) and R. Lazarsfeld (University of Michigan). The main topics considered were vanishing theorems, multiplyer ideal sheaves and effective results in algebraic geometry, tight closure, geometry of higher dimensional projective and Köhler manifolds, hyperbolic algebraic varieties. The school consisted of two weeks of lectures and one week of conference. Thisvolume contains the lecture notes of most of the lectures in the first two weeks. (ISBN 92-95003-09-8)