This is the first volume of a new series of lecture notes of the Abdus Salam International Centre for Theoretical Physics. These new lecture notes are put onto the web pages of the ICTP to allow people from all over the world to access them freely. In addition a limited number of hard copies is printed to be distributed to scientists and institutions which otherwise possibly do not have access to the web pages. This first volume contains the lecture notes of the School on Algebraic Geometry which took place at the Abdus Salam International Centre for Theoretical Physics from 26 July to 13 August 1999 under the direction of Lothar Göttsche (ICTP), Joseph Le Potier (Universite Paris 7), Eduard Looijenga (University of Utrecht), M.S. Narasimhan (ICTP). The school consisted of 2 weeks of lecture courses and one week of conference. This volume contains the notes of most of the lecture courses in the first two weeks. The topic of the school was moduli spaces. More specifically the lectures were devided into three subtopics: principal bundles on Riemann surfaces, moduli spaces of vector bundles and sheaves on projective varieties, and moduli spaces of curves. (ISBN 92-95003-00-4)