This unified account of various aspects of a powerful classical
method, easy to understand in its simplest forms, is illustrated by
applications in several areas of number theory. As well as
including diophantine approximation and transcendence, which were
mainly responsible for its invention, the author places the method
in a broader context by exploring its application in other areas,
such as exponential sums and counting problems in both finite
fields and the field of rationals. Throughout the book, the method
is explained in a 'molecular' fashion, where key ideas are
introduced independently. Each application is the most elementary
significant example of its kind and appears with detailed
references to subsequent developments, making it accessible to
advanced undergraduates as well as postgraduate students in number
theory or related areas. It provides over 700 exercises both
guiding and challenging, while the broad array of applications
should interest professionals in fields from number theory to
algebraic geometry.
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