Sieve methods form one of pillars of contemporary number theory. The aim of this monograph is to provide a concise treatment of integer and half integer dimensional sieves, which extends Jurkat and Richert’s original method for dimension 1. The book is written very carefully, giving all the necessary details (or at least hints), as this is a highly technical topic. A very interesting feature of the book is the appendix “Procedures for computing sieve functions“, containing details of programs of the Mathematica software package for sieve-theory calculations, which is accessible on the authors' website. The monograph is a very good source of details of techniques used in sieve methods and their applications, and therefore it can be warmly recommended for everyone interested in sieve methods.