An Introduction to the Theory of Numbers by G. H. Hardy and E. M. Wright is found on the reading list of virtually all elementary number theory courses and is widely regarded as the primary and classic text in elementary number theory. Developed under the guidance of D. R. Heath-Brown, this Sixth Edition of An Introduction to the Theory of Numbers has been extensively revised and updated to guide today's students through the key milestones and developments in number theory.Updates include a chapter by J. H. Silverman on one of the most important developments in number theory - modular elliptic curves and their role in the proof of Fermat's Last Theorem -- a foreword by A. Wiles, and comprehensively updated end-of-chapter notes detailing the key developments in number theory. Suggestions for further reading are also included for the more avid reader.The text retains the style and clarity of previous editions making it highly suitable for undergraduates in mathematics from the first year upwards as well as an essential reference for all number theorists.Roger Heath-Brown F.R.S. was born in 1952, and is currently Professor ofPure Mathematics at Oxford University. He works in analytic numbertheory, and in particular on its applications to prime numbers and toDiophantine equations.Preface to the sixth edition Andrew WilesPreface to the fifth edition1. The Series of Primes (1)2. The Series of Primes (2)3. Farey Series and a Theorem of Minkowski4. Irrational Numbers5. Congruences and Residues6. Fermat's Theorem and its Consequences7. General Properties of Congruences8. Congruences to Composite Moduli9. The Representation of Numbers by Decimals10. Continued Fractions11. Approximation of Irrationals by Rationals12. The Fundamental Theorem of Arithmetic in k(l), k(i), and k(p)13. Some Diophantine Equations14. Quadratic Fields (1)15. Quadratic Fields (2)16. The Arithmetical Functions ø(n), m(n), d(n), s(n), r(n)17. Generating Functions of Arithmetical Functions18. The Order of Magnitude of Arithmetical Functions19. Partitions20. The Representation of a Number by Two or Four Squares21. Representation by Cubes and Higher Powers22. The Series of Primes (3)23. Kronecker's Theorem24. Geometry of Numbers25. Elliptic Curves, Joseph H. SilvermanAppendixList of BooksIndex of Special Symbols and WordsIndex of NamesGeneral Index