1. The Structure of Sifting Arguments.- 2. Selberg's Upper Bound Method.- 3. Combinatorial Methods.- 4. Rosser's Sieve.- 5. The Sieve with Weights.- 6. The Remainder Term in the Linear Sieve.- 7. Lower Bound Sieves when ? > 1.- References.

This book surveys the current state of the "small" sieve methods developed by Brun, Selberg and later workers. The book is suitable for university graduates making their first acquaintance with the subject, leading them towards the frontiers of modern research and unsolved problems in the subject area.