This book by Polya and Szego contains many wonderful gems of mathematics. The exercises are very interesting, and sometimes I pick the book up just for fun. I wish I had been able to purchase a hardcover copy. Unfortunately, it's only available in paperback.

This book is suitable for mathematics graduate students.

The selected problems aren't the typical ones. The great beauty of many results are marvellous and, disposed in dificulty ascendent, are teh best way to start researches. I teach in the University of Málaga and I'm interested in the second vol.

Polya and Szego's 1923 two volumes of mathematics problems are still the best collections of problems for people who want to learn advanced undergraduate and graduate level mathematics. When I want to know something about zeros of polynomials, about inequalities for polynomials or trigonometric polynomials, or determinants and quadratic forms, the first place I look is volume 2 of Polya and Szego. It is a great source of problems to give to students if you are a teacher, and the best set of problems to work through if you are learning mathematics at the advanced undergraduate level or higher. Volume 2 contains long chapters on complex variables and number theory and some problems in geometry. Both volumes belong on a shelf close to the desk of anyone who teaches college level mathematics. They are also very useful for those who use mathematics. These two volumes are gems, and would be rated above 5 stars if possible. The German original is available here in a nice English translation. Some new material was added when the translation was first published.