to Rational Points on Plane Curves. - Elementary Properties of the Chord-Tangent Group Law on a Cubic Curve. - Plane Algebraic Curves. - Elliptic Curves and Their Isomorphisms. - Families of Elliptic Curves and Geometric Properties of Torsion Points. - Reduction mod p and Torsion Points. - Proof of Mordell's Finite Generation Theorem. - Galois Cohomology and Isomorphism Classification of Elliptic Curves over Arbitrary Fields. - Descent and Galois Cohomology. - Elliptic and Hypergeometric Functions. - Theta Functions. - Modular Functions. - Endomorphisms of Elliptic Curves. - Elliptic Curves over Finite Fields. - Elliptic Curves over Local Fields. - Elliptic Curves over Global Fields and ?-Adic Representations. - L-Function of an Elliptic Curve and Its Analytic Continuation. - Remarks on the Birch and Swinnerton-Dyer Conjecture. - Remarks on the Modular Elliptic Curves Conjecture and Fermat's Last Theorem. - Higher Dimensional Analogs of Elliptic Curves: Calabi-Yau Varieties. - Families of Elliptic Curves. Language: English