This book presents pedagogical contributions on selected topics relating Number Theory, Theoretical Physics and Geometry. The parts are composed of long self-contained pedagogical lectures followed by shorter contributions on specific subjects organized by theme. Most courses and short contributions go up to the recent developments in the fields; some of them follow their author?s original viewpoints. There are contributions on Random Matrix Theory, Quantum Chaos, Non-commutative Geometry, Zeta functions, and Dynamical Systems. The chapters of this book are extended versions of lectures given at a meeting entitled Number Theory, Physics and Geometry, held at Les Houches in March 2003, which gathered mathematicians and physicists.