This is a valuable resource of problems and strategies for the advanced problem solver. Informally written tidbits throughout the text warn students of possible traps, encourage formal proof, and also provide glimpses into the history of mathematics. From number theory to algebra, the book has a broad collection of problems. Many of the problems are taken from challenging contests, including MAA contests, Mathcounts, Mandelbrot competition and others. Complete solutions are found in The Art of Problem Solving Vol. 2: And Beyond, Solutions.