Nicomachus of Gerasa's Introduction to Arithmetic translated into English by Martin Luther D'Ooge with studies in Greek Arithmetic by Frank Egleston Robbins and Louis Charles Karpinski is a translated and expanded edition of Nicomachus's Introduction to Arithmetic, a seminal text in ancient Greek mathematics. Initially left incomplete due to the sudden death of Martin Luther D'Ooge, the translation was finished and supplemented by his colleagues at the University of Michigan. Frank Egleston Robbins and Louis Charles Karpinski contributed to completing the supporting studies and final revisions. This comprehensive volume comprises three parts: studies in Greek mathematics, a direct translation of Nicomachus's work, and supplementary aids for interpretation, including extensions of Nicomachus's theorems, a glossary of Greek terms, and a bibliography. The book delves into the origins, development, and influence of Greek arithmetic, highlighting its philosophical significance beyond mere computational skills. It traces the roots of Greek mathematical knowledge, discussing influences from Egypt and Babylon, and examines the philosophical arithmetic focused on number theory rather than practical computation. The translation captures Nicomachus's work's intricate details, illustrating the interconnectedness of arithmetic, geometry, and music in Greek thought, and offers modern scholars a valuable perspective on ancient mathematical approaches.