ABSTRACT
This introduction presents an overview of the key concepts discussed in the subsequent chapters of this book. The book deals with most of the background in algebraic geometry. It provides foundational results in commutative algebra that are needed for the development of the theory of algebraic varieties. The book introduces the Zariski topology of the affine space; this topology has as closed sets the algebraic subsets. It describes the first notions of the theory of algebraic varieties. The book defines the notion of a sheaf on a topological space, centering our attention on sheaves of functions. The concept of prevariety is then strengthened in order to introduce the main geometrical object of study, algebraic varieties. Hilbert's Nullstellensatz is one of the basic building blocks of the theory of algebraic varieties, and should be considered as a deep generalization of the so-called fundamental theorem of algebra.
