Two volume work containing a contemporary account on Positivity in Algebraic Geometry

A good deal of the material has not previously appeared in book form

Volume I is more elementary than Volume II and can be read without access to Volume II

Topics in Volume I: ample line bundles and linear series on a projective variety, the classical theorems of  Lefschetz and Bertini, vanishing theorems, local positivity

Contains many concrete examples, applications, and pointers to further developments