OverthemillenniaDiophantineequationshavesuppliedanextremelyfertilesource ofproblems. Their study hasilluminated everincreasingpoints ofcontactbetween very di?erent subject areas, including algebraic geometry, mathematical logic, - godictheoryandanalyticnumber theory. Thefocus ofthis bookisonthe interface of algebraic geometry with analytic number theory, with the basic aim being to highlight the ro le that analytic number theory has to play in the study of D- phantine equations. Broadly speaking, analytic number theory can be characterised as a subject concerned with counting interesting...