In many instances, due to exigencies of simplicity and rigor, the proofs given in the text differ, to a greater or less extent, from the proofs given in the original papers.

This book examines three pairs of proofs of the theorem from three different areas of mathematics: abstract algebra, complex analysis and topology.

This book can thus be used as textbook for an introductory course in algebraic geometry following a basic graduate course in algebra.

This new edition also includes an overview of the theory of curves, their moduli spaces and their Jacobians, one of the most exciting fields within algebraic geometry.