Includes bibliographical references and index.

Introduction -- A crash course in commutative algebra -- Ane varieties -- Projective varieties -- Regular and rational maps of quasi projective varieties -- Products -- The blow up of an ideal -- Finite maps of quasi projective varieties -- Dimension of quasi projective algebraic sets -- Zariski's main theorem -- Nonsingularity -- Sheaves -- Applications to regular and rational maps -- Divisors -- Dierential forms and the canonical divisor -- Schemes -- The degree of a projective variety -- Cohomology -- Curves -- An introduction to intersection theory -- Surfaces -- Ramication and etale maps -- Bertini's theorems and general fibers of maps.