This second volume is a comprehensive treatment of Diophantine analysis. Besides the familiar cases of Diophantine equations, this rubric also covers partitions, representations as a sum of two, three, four or $n$ squares, Waring's problem in general and Hilbert's solution of it, and perfect squares in arithmetical and geometrical progressions. Of course, many important Diophantine equations, such as Pell's equation, and classes of equations, such as quadratic, cubic and quartic equations, are treated in detail. As usual with Dickson, the account is encyclopedic and the references are numerous.