This book reproduces, with minor changes, the notes prepared for a
course given at Brigham Young University during the academic year
1984-1985. It is intended to be an introduction to the theory of
numbers. The audience consisted largely of undergraduate students with
no more background than high school mathematics. The presentation was
thus kept as elementary and self-contained as possible. However, because
the discussion was, generally, carried far enough to introduce the
audience to some areas of current research, the book should also be
useful to graduate students. The only prerequisite to reading the book
is an interest in and aptitude for mathe- matics. Though the topics may
seem unrelated, the study of diophantine equations has been our main
goal. I am indebted to several mathematicians whose published as well as
unpublished work has been freely used throughout this book. In
particular, the Phillips Lectures at Haverford College given by
Professor John T. Tate have been an important source of material for the
book. Some parts of Chapter 5 on algebraic curves are, for example,
based on these lectures.