Atle Selberg's early work, which lies in the fields of analysis and number theory, 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 is in the finest classical tradition. His later work, which cuts across function theory, operator theory, spectral theory, group theory, topology, differential geometry and number theory, has enlarged and transfigured the whole concept and structure of arithmetic. It exemplifies the modern tradition at its sprightly best and reveals Selberg to be one of the master mathematicians of our time. This 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. The second volume contains material on which Selberg has lectured - some later papers from 1988 onward and, in the major part, the "Lectures on Sieves".