This book is dedicated to George Polya, who focused on problem solving as the means for teaching and learning mathematics. The first chapter is a reprint of his article "On Learning, Teaching, and Learning Teaching." Then, G. L. Alexanderson paints a portrait of "George Polya, Teacher," including some anecdotes that exemplify Polya's art of teaching. Alan Schoenfeld, in "A Brief and Biased History of Problem Solving," traces problem-solving developments from Socrates to the present, with note of how Polya will continue to influence further development. In "Discovering, Modifying, and Solving Problems: A Case Study from the Contemplation of Polyhedra," Peter Hilton and Jean Pedersen discuss Polya's emphasis on problem solving as a process that leads to more questions and problems. Lester Lange continues this idea in "Polya's 'Mushrooms' -- a Mathematical Concert Remembering George Polya." Polya's views about teacher training are discussed by Jeremy Kilpatrick in "Is Teaching Teachable? George Polya's Views on the Training of Mathematics Teachers." Finally, Marilyn Suydam reviews research from the 1980s on problem solving in "Indications from Research on Problem Solving." A "Chronological Bibliography of Polya's Work in Mathematics Education" is included in the appendix. (MNS)