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Table of Contents

Generalities.- Some noncommutative Algebra.- Graded rings.- The finishing touch on localization.- Structure sheaves and schemes.- Algebraic varieties.- Coherent and quasicoherent sheaves of modules over an algebraic k-variety.- Products, subvarieties etc....- Representation theory revisited.- Birationality and quasivarieties.- A non-commutative version of the riemann-roch theorem for curves.- Work in progress, [91].