The first volume of Pólya's papers deals with singular points of analytic functions and with other broadly related topics, such as conformal mappings, entire functions, and the rate of growth of analytic functions. The papers are arranged in chronological order, but the editor, in his introduction, shows that they fall into four main sets of topics.
The first is concerned with properties of a function (in particular, the location and nature of its singular points) as deduced from the properties of the coefficients in its power series.
A second set deals with a closely related problem: connections between global properties of a function and its values at an isolated set of points. Analytic functions, especially entire functions, are the subject of a third set of papers, and a final set of six investigates problems in conformal mapping.
The papers in this volume cluster about the following topics: the location of the zeros of polynomials and other analytic functions; the approximation of analytic functions by polynomials in which the location of zero is restricted (these papers represent some of Pólya's most influential work); the behavior of the zeros of successive derivatives; the zeros of functions defined by trigonometric integrals; and the signs of derivatives and their analytic character.
The volume also includes a paper that is not about zeros but contains a representation theorem for positive polynomials in several variables.