This is a translation of a book originally published in 1932 under the title Triumph der Mathematik. The original title was better. Most of the problems here are far from elementary. For example, there is a nine-page proof of the Hermite-Lindemann theorem on the transcendence of pi and e, and a 12-page proof of Abel's theorem on the insolvability in closed form of equations higher than fourth degree. These are not what you normally call elementary problems. To understand them, and to understand their solutions, one might do better to consult more specialized texts in the areas under discussion.
On the other hand, the book is a gold mine of fascinating mathematics: How much must a sailboat tack with a north wind in order to get north as quickly as possible? From the altitude of two known stars determine your time and position. Construct the five regular solids. Prove that of all solids of equal surface the sphere possesses the maximum volume. Determine pi experimentally by throwing a needle across parallel lines.
The selection of problems is outstanding and lives up to the book's original title. The proofs are concise, clever, elegant, often extremely difficult and not particularly enlightening. To say that this book requires a background in college math is like saying that playing chess requires a background in how to move the pieces; it also requires a lot of thought and, preferably, a lot of experience.
I would recommend this book to practicing mathematicians, both amature and professional. For the rest of us, the author has surveyed more than 2,000 years of mathematical problems and picked out some real beauties.