This monograph, titled "Gaussian Measures in Banach Spaces," is based on lecture notes from a course titled "Applications of Measure Theory" given at the University of Virginia in the spring of 1974. The primary focus is on introducing the concept of abstract Wiener space and exploring related topics. The first two chapters and the first three sections of Chapter III were covered in the course, with the remaining sections added during the rewriting process. The author expresses regret for not including recent works on integration on Banach manifolds by J. Bell, K.D. Elworthy, and R. Ramer, among others. The book covers topics such as Hilbert-Schmidt and trace class operators, Borel measures in Hilbert spaces, Wiener measure and integral, abstract Wiener spaces, weak distribution, and Gross-Sazonov theorem. It also discusses equivalence and orthogonality of Gaussian measures, translation of Wiener measure, Kakutani's theorem, Feldman-Hajek's theorem, and various results about abstract Wiener spaces, including potential theory and stochastic integrals. The author acknowledges the support of Professor Leonard Gross, Professor Kiyosi Ito, and others for their encouragement and contributions.This monograph, titled "Gaussian Measures in Banach Spaces," is based on lecture notes from a course titled "Applications of Measure Theory" given at the University of Virginia in the spring of 1974. The primary focus is on introducing the concept of abstract Wiener space and exploring related topics. The first two chapters and the first three sections of Chapter III were covered in the course, with the remaining sections added during the rewriting process. The author expresses regret for not including recent works on integration on Banach manifolds by J. Bell, K.D. Elworthy, and R. Ramer, among others. The book covers topics such as Hilbert-Schmidt and trace class operators, Borel measures in Hilbert spaces, Wiener measure and integral, abstract Wiener spaces, weak distribution, and Gross-Sazonov theorem. It also discusses equivalence and orthogonality of Gaussian measures, translation of Wiener measure, Kakutani's theorem, Feldman-Hajek's theorem, and various results about abstract Wiener spaces, including potential theory and stochastic integrals. The author acknowledges the support of Professor Leonard Gross, Professor Kiyosi Ito, and others for their encouragement and contributions.