Algorithmic Number Theory provides a thorough introduction to the design and analysis of algorithms for problems from the theory of numbers. Although not an elementary textbook, it includes over 300 exercises with suggested solutions. Every theorem not provided in the text or left as an exercise has a reference in the notes section that appears at the end of each chapter. The bibliography contains over 1750 citations to the literature. Finally, it blends computational theory with practice by covering some of the practical aspects of algorithm implementations.