The early work of Atle Selberg lies in the fields of analysis and number theory. It concerns the Riemann zeta-function, Dirichlet's L-functions, the Fourier coefficients of modular forms, the distribution of prime numbers, and the general sieve method. It is brilliant, and unsurpassed, and in the finest classical tradition. His later work cuts across many fields: function theory, operator theory, spectral theory, group theory, topology, differential geometry, and number theory. It has enlarged and transfigured the whole concept and structure of arithmetic. It exemplifies the modern tradition at its sprightly best, and makes him one of the master mathematicians of our time. This outstanding publication will enable the reader to perceive the depth and originality of Atle Selberg's ideas and results, and sense the scale and intensity of their influence on contemporary mathematical thought.