Diophantine geometry has been studied by number theorists for
thousands of years, since the time of Pythagoras, and has continued
to be a rich area of ideas such as Fermat's Last Theorem, and most
recently the ABC conjecture. This monograph is a bridge between the
classical theory and modern approach via arithmetic geometry. The
authors provide a clear path through the subject for graduate
students and researchers. They have re-examined many results and
much of the literature, and give a thorough account of several
topics at a level not seen before in book form. The treatment is
largely self-contained, with proofs given in full detail. Many
results appear here for the first time. The book concludes with a
comprehensive bibliography. It is destined to be a definitive
reference on modern diophantine geometry, bringing a new standard
of rigor and elegance to the field.
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