One of the most effective ways to stimulate students to enjoy intellectual efforts is the scientific competition. In 1894, the Hungarian Mathematical and Physical Society introduced a mathematical competition for high school students. Among the winners were Lipot Fejer, Alfred Haar, Todor Karman, Marcel Riesz, Gabor Szego, and many others who became world-famous scientists. The success of high school competitions led the Mathematical Society to found a college-level contest, named after Miklos Schweitzer. The problems of the Schweitzer contests are proposed and selected by the most prominent Hungarian mathematicians. This book collects the problems posed in contests between 1962 and 1991, which range from algebra, combinatorics, theory of functions, geometry, measure theory, number theory, operator theory, probability theory, and topology to set theory. Solutions are included. The Schweitzer competition is one of the most unique in the world. Experience shows that this competition helps identify research talents. This collection of problems and solutions in several fields in mathematics can serve as a guide for many undergraduates and young mathematicians. The large variety of research-level problems should interest more mature mathematicians and historians of mathematics as well.