Algebraic Geometry I - Complex Projective Varieties (Paperback, Reprint of the 1st ed. Berlin, Heidelberg, New York 1976. Corr. 2nd printing 1981.)

From the reviews: "Although several textbooks on modern algebraic geometry have been published in the meantime, Mumford's "Volume I" is, together with its predecessor the red book of varieties and schemes, now as before one of the most excellent and profound primers of modern algebraic geometry. Both books are just true classics " Zentralblatt