Heights in Diophantine Geometry

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 Fermats 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.