"A Classical Introduction to Modern Number Theory" is a revised and expanded version of "Elements of Number Theory" published in 1972. The book is intended for upper-level undergraduate mathematics majors and graduate students, assuming some familiarity with abstract algebra. It covers a wide range of topics in number theory, focusing on algebraic number theory and arithmetic algebraic geometry. The content includes prime numbers, unique factorization, arithmetic functions, congruences, quadratic reciprocity, and reciprocity laws. The book also discusses diophantine equations over finite fields and rational numbers, as well as zeta functions, including the Riemann zeta function and Dirichlet L-functions. It includes historical notes, references, and a comprehensive bibliography. The book emphasizes the historical development of number theory and provides a wealth of material for further study. It includes many exercises, some routine and some challenging, which help reinforce the concepts discussed. The authors thank their colleagues and friends for their assistance in the writing of the book. The book is structured into chapters covering various topics in number theory, including unique factorization, congruences, quadratic reciprocity, Gauss and Jacobi sums, finite fields, cubic and biquadratic reciprocity, equations over finite fields, zeta functions, algebraic number theory, quadratic and cyclotomic fields, Bernoulli numbers, Dirichlet L-functions, diophantine equations, and elliptic curves. The book is a comprehensive introduction to modern number theory, combining classical and modern topics with a focus on the historical development of the subject."A Classical Introduction to Modern Number Theory" is a revised and expanded version of "Elements of Number Theory" published in 1972. The book is intended for upper-level undergraduate mathematics majors and graduate students, assuming some familiarity with abstract algebra. It covers a wide range of topics in number theory, focusing on algebraic number theory and arithmetic algebraic geometry. The content includes prime numbers, unique factorization, arithmetic functions, congruences, quadratic reciprocity, and reciprocity laws. The book also discusses diophantine equations over finite fields and rational numbers, as well as zeta functions, including the Riemann zeta function and Dirichlet L-functions. It includes historical notes, references, and a comprehensive bibliography. The book emphasizes the historical development of number theory and provides a wealth of material for further study. It includes many exercises, some routine and some challenging, which help reinforce the concepts discussed. The authors thank their colleagues and friends for their assistance in the writing of the book. The book is structured into chapters covering various topics in number theory, including unique factorization, congruences, quadratic reciprocity, Gauss and Jacobi sums, finite fields, cubic and biquadratic reciprocity, equations over finite fields, zeta functions, algebraic number theory, quadratic and cyclotomic fields, Bernoulli numbers, Dirichlet L-functions, diophantine equations, and elliptic curves. The book is a comprehensive introduction to modern number theory, combining classical and modern topics with a focus on the historical development of the subject.