Edition focuses on addressing the question of when a prime p is of the form x2 + ny2, which serves as the basis for further discussion of various mathematical topics. This updated edition has several new notable features, including: * A well-motivated introduction to the classical formulation of class field theory * Illustrations of explicit numerical examples to demonstrate the power of basic theorems in various situations * An elementary treatment of quadratic forms and genus theory * Simultaneous treatment of elementary and advanced aspects of number theory * New coverage of the Shimura reciprocity law and a selection of recent work in an updated bibliography Primes of the Form p = x2 + ny2, Second Edition is both a useful reference for number theory theorists and an excellent text for undergraduate and graduate-level courses in number and Galois theory.