This volume focuses primarily on those problems from number theory that admit relatively efficient solutions. The second volume will largely focus on problems for which efficient algorithms are not known, and applications thereof. We hope that the material in this book will be useful for readers at many levels, from the beginning graduate student to experts in the area.
Later chapters assume some familiarity with Galois theory.
As stated above, this book discusses the current state of the art in algorithmic number theory. This book is not an elementary number theory textbook, and so we frequently do not give detailed proofs of results whose central focus is not computational. Choosing otherwise would have made this book twice as long. However, we firmly believe that a mere list of proved theorems is not particularly enlightening or useful. Therefore, we endeavor to prove as much as is feasible.