Abstract
The approximation space definition has evolved in rough set theory over the last 15 years. The aim was to build a unified framework for concept approximations. We present an overview of this evolution together with some operations on approximation spaces that are used in searching for relevant approximation spaces. Among such operations are inductive extensions and granulations of approximation spaces. We emphasize important consequences of the paper for research on approximation of vague concepts and reasoning about them in the framework of adaptive learning. This requires developing new approach to vague concepts going beyond the traditional rough or fuzzy approaches.