Abstract. Suppose that X, Y are Banach spaces. A mapping f : X → Y is said to be an isometry provided k f(x) ? f(y)k = kx ? yk, ?x, y ∈ X. Because of its profundity in theory and universality in application, the study of isometry and its generalizations of Banach spaces has continued for over 90 years. In this talk, we will give a historical overview of this research area, and mainly focus on the progress in the last two decades, including some contributions of the FA group at Xiamen University.
