This book was first published in 1952. It is largely devoted to the object of proving the Vinogradov-Goldbach theorem: that every sufficiently large odd number is the sum of three primes. In the course of proving this, T. Estermann, formerly Professor of Mathematics at the University of London, supplies numerous theories and results on characters and primes in arithmetic progressions. The author also ensures that the proofs presented to the reader are both clear and remarkably concise. The volume at hand addresses the Riemann zeta function, primes in arithmetical progression, and the ways in which odd numbers can be represented as the sum of three primes. At the end of the book is an index and a seven-page section of theorems and formulae for reference. This volume is both interesting and accessible, and will appeal to all with an enthusiasm for mathematics and problem solving.