This textbook offers an invitation to modern algebra through number systems of increasing
complexity beginning with the natural numbers and culminating with Hamilton's quaternions.
Along the way the authors carefully develop the necessary concepts and methods from abstract
algebra: monoids groups rings fields and skew fields. Each chapter ends with an appendix
discussing related topics from algebra and number theory including recent developments
reflecting the relevance of the material to current research. The present volume is intended
for undergraduate courses in abstract algebra or elementary number theory. The inclusion of
exercises with solutions also makes it suitable for self-study and accessible to anyone with an
interest in modern algebra and number theory.
