Diophantine Approximations and Diophantine Equations

This monograph studies diophantine approximations to algebraic numbers and their applications to diophantine equations. The methods are classical, and the results stressed can be obtained without much background in algebraic geometry. In particular, Thue equations, norm form equations and S-unit equations, with emphasis on recent explicit bounds on the number of solutions, are included. Reader require no background knowledge beyond a rudimentary understanding of algebraic number theory.