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Elliptic Curves (Graduate Texts In Mathematics, 111),New Snay Stepbystep System For Mastering TheThere Are Three New Appendices, One By Stefan Theisen On The Role Of Calabi Yau Manifolds In String Theory And One By Otto Forster On The Use Of Elliptic Curves In Computing Theory And Coding Theory. In The Third Appendix We Discuss The Role Of Elliptic Curves In Homotopy Theory. In These Three Introductions The Reader Can Get A Clue To The Farreaching Implications Of The Theory Of Elliptic Curves In Mathematical Sciences. During The ? Nal Production