Abstract : A Lecture Series in Modern Analysis and Applications was sponsored by the Consortium of American, Catholic, Georgetown, George Washington and Howard Universities, of the District of Columbia, the University of Maryland, College Park, and the Air Force Office of Scientific Research, in the greater Washington, D. C. area, during the period Fall, 1967 through Spring 1969. The series consisted of 8 sessions of 3 lectures each. Each session was devoted to an active basic area of contemporary analysis which is important in application or shows potential applications. Each lecture presented a survey and a critical review of certain aspects of that area, with emphasis on new results, open problems and applications. This volume, the third and final one of the series, contains five lectures from the seventh and eighth sessions, which were devoted to modern harmonic analysis and applications, and integration in function spaces and applications. The lectures concern the Littlewood-Paley Theory, the Theory of Automorphic Forms, Quantization and Unitary Representations, Random Linear Functionals, and the Absolute Continuity of Stochastic Processes. (Author)