A Classical Introduction to Modern Number Theory is a comprehensive textbook that bridges the gap between elementary number theory and the systematic study of advanced topics. It is aimed at readers who have a fundamental understanding of abstract algebra. The book places particular emphasis on the historical development of number theory and provides a broad coverage of significant results, supported by relatively elementary proofs, some of which are new. The second edition includes corrections as well as two new chapters that offer a complete proof of the Mordell-Weil theorem for elliptic curves over the rational numbers and an overview of recent advances in the arithmetic of elliptic curves. Additionally, the book features an extensive bibliography and numerous challenging exercises that deepen the understanding of the topics covered.