"An Introduction to Number Theory" offers a comprehensive introduction to the central currents of number theory. The book begins with the unique factorization property of integers and revisits factorization throughout to illustrate how the ideas from Euclid continue to influence the field today. Various approaches to number theory are presented, and the different strands of the book converge in a chapter that describes the class number formula for quadratic fields and the famous conjectures of Birch and Swinnerton-Dyer. The concluding chapter introduces some of the fundamental ideas of modern computational number theory and their applications in cryptography. This textbook is aimed at graduate students and advanced undergraduates in mathematics, but it is also of interest to students in related fields who wish to learn the essential concepts of number theory.