Diophantine Approximation: Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 28 – July 6, 2000

Diophantine Approximation is a branch of Number Theory having its origins in the problem of producing “best” rational approximations to given realn- bers. Since the early work of Lagrange on PellÂ’s equation and the pioneering work of Thue on the rational approximations to algebraic numbers of degree ? 3, it has been clear how, in addition to its own speci?c importance and – terest, the theory can have fundamental applications to classical diophantine problems in Number Theory.