ABSTRACT
This chapter gives a survey of some results on diophantine approximation and their applications. It contains an introduction to the theory of linear forms in logarithms of algebraic numbers, and describes some results following from the Subspace Theorem. The chapter gives applications to the local behaviour of sequences of numbers composed of small primes and of sums of two such numbers. It deals with the transcendence of infinite sums of values of a rational function and related sums, and some recent applications to diophantine equations and recurrence sequences are described. There has been a tremendous stream of important results on diophantine equations in the past decades, culminating in the proof of Fermat’s Last Theorem by Wiles and Taylor.
