This book is a translation of the second Polish edition, published in 1960, in which various improvements were made. The contest for secondary school pupils known as the Mathematical Olympiad has been held in Poland every year since 1949/50. The problems set at the contests require only a knowledge of school mathematics (i.e., elementary algebra, geometry and trigonometry) but are on the whole more difficult than the usual school exercises. COMMENT: Although long out of print and hard to find, this is MUST read for aspiring contestants in the AMC/AIME/USAME mathematics contests. If you only have time for a couple of books to review and study, this should be one of them.