Introduction to Modern Number Theory : Fundamental Problems

Problems and Tricks.- Number Theory.- Some Applications of Elementary Number Theory.- Ideas and Theories.- Induction and Recursion.- Arithmetic of algebraic numbers.- Arithmetic of algebraic varieties.- Zeta Functions and Modular Forms.- Fermats Last Theorem and Families of Modular Forms.- Analogies and Visions.- Introductory survey to part III: motivations and description.- Arakelov Geometry and Noncommutative Geometry (daprès C. Consani and M. Marcolli, [CM]).