Addressed to specialists, teachers, and advanced students in statistics who are acquainted with the basic facts about the theory of testing hypotheses, measure theory, stochastic processes, and the central limit theorem. Concentrates on continuous alternatives and on problems concerning location and scale parameters. The first edition was published in 1967, but H<'a>jek died young in 1974 and not until now has his co-author found another collaborator to update the treatment to account for the considerable developments over the intervening three decades. Some elements of the organization and style have also been changed.