These two volumes complete the publication of the collected papers of George Polya, one of the most influential mathematicians and teachers of our time. Volumes I (Singularities of Analytic Functions) and II (Location of Zeros) were published in 1974. Volume III contains 58 papers spanning Polya's career (the earliest is from 1913, the latest from 1976) and covering a wide range of subjects in mathematical analysis and mathematical physics. The commentaries on these papers attest to the fertility and continued importance of Polya's ideas in current mathematics. Volume IV presents 20 papers on probability, 17 on combinatorics, and 18 on the teaching and learning of mathematics. Polya has made a number of fundamental contributions to the first two fields, including perhaps the first use of the term "central limit theorem," but his major influence on mathematics has clearly been his approach to pedagogy. Many of the papers throughout these volumes have a strongly pedagogical flavor, but the papers in the third section of this volume focus squarely on the real business of how to do mathematics - how to formulate a problem and then create a solution. George Polya is professor emeritus at Stanford University. These volumes are the twenty-second and twenty-third in the series Mathematicians of Our Time, edited by Gian-Carlo Rota.