The International Mathematics Tournament of the Towns is a mathematics competition for junior and senior high school students all over the world. The tournament began in 1980 in the former Soviet Union. Participants write contest papers locally, with emphasis on solving within a very generous time allowance a small number of interesting problems. The tournament does not offer prizes, in order to de-emphasize its competitive aspect, though diplomas, certificates, and books are distributed to deserving participants. Supplementary activities include a year-round correspondence school and a summer school in Russia. A description of a participant at the summer school, which was hosted by the Beloretsk Computer School, is appended. Three of the problems proposed at the summer school are included. A selection of 50 problems from the tournaments for junior high students is also appended. (JDD)