Yuri Ivanovich Manin is a senior staff member at the Steklov Institute of the Academy of Sciences of the USSR and Professor at the University of Moscow. He is best known for his work in number theory and algebraic geometry; for the latter, he was awarded the Lenin Prize in 1967 when he was 30 years old. Professor Manin received his mathematical education at the University of Moscow from which he graduated in 1958 and obtained his Ph.D. in 1963. The present book developed from a course of lectures and reflects the author's exceptionally wide perspective of the subject. The topics which are discussed range from very modern problems in mathematical logic to quantum logic, the finite presentation of groups and linguistic and philosophical questions.