Arithmetic Algebraic Geometry : Lectures given at the 2nd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Trento Italy June 24–July 2 1991 This volume contains three long lecture series by J.L. Colliot Thelene Kazuya Kato and P. Vojta. Their topics are respectively the connection between algebraic K theory and the torsion algebraic cycles on an algebraic variety a new approach to Iwasawa theory for Hasse Weil L function and the applications of arithemetic geometry to Diophantine approximation. They contain many new results at a very advanced level but also surveys of the state of the art on the subject with complete detailed profs and a lot of background. Hence they can be useful to readers with very different background and experience. CONTENTS: J.L. Colliot Thelene: Cycles algebriques de torsion et K theorie algebrique. K. Kato: Lectures on the approach to Iwasawa theory for Hasse Weil L functions. P. Vojta: Applications of arithmetic algebraic geometry to diophantine approximations