This book covers thirty years of the Leningrad Mathematical Olympiad, which was, ostensibly, the very first formally organized, open, official city-level mathematical contest in the world. Founded in 1934 by a group of dedicated Soviet mathematicians, it played an outstanding (and often underappreciated) role in creating the Leningrad (St. Petersburg) school of mathematics of the 20th century.The book begins with the extensive introduction containing two prefaces (one of them written specifically for this edition), a large historical survey of the Leningrad Mathematical Olympiad, a section describing the logistical side of the contest, and a small chapter dedicated to the very first Mathematical Olympiad held in 1934, whose problems were recently found in the Soviet-era library archives.The main text contains approximately 1,100 highly original questions for students of grades 5 through 10 (ages 11–12 through 17–18) offered at the two concluding rounds of the Leningrad City Mathematics Olympiads in the years of 1961–1991. Full solutions, hints and answers are provided for all questions with very rare exceptions.It also includes 120 additional questions, offered at the various mathematical contests held in Leningrad over the same thirty-year period — on average, their difficulty is somewhat higher than that of the regular Mathematical Olympiad problems.