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This book offers a self-contained elementary introduction to the fundamental concepts and techniques of Algebraic Geometry, leading to some gems of the subject like Bezout’s Theorem, the Fundamental Theorem of Projective Geometry, and Zariski’s Main Theorem. The book contains a detailed treatment of algebraic plane curves with a special emphasis on elliptic curves and their birational classification. The role played by elliptic curves in modern theory of ...