This volume contains many of the papers in the area of algebraic geometry presented at the 1984 Solomon Lefschetz Centennial Conference held in Mexico City. It is the first in a three volume series. The conference focused on this topic along with the areas of algebraic topology and differential equations where Lefschetz made significant contributions. The proceedings begin with two interesting articles: A Page of Mathematical Autobiography, that has been reprinted from an early edition of the Bulletin of the AMS, and ``Solomon Lefschetz, a biography'' by William Hodge, that is reprinted from the Bulletin of the London Mathematical Society.