Rough set theory is a formal approach to vagueness and imprecision that was introduced in the mid eighties of the previous century by Zdislaw Pawlak. The subject has grown tremendously in pure and applied directions from mathematical, algebraic logical, logical, philosophical and computational perspectives. The present author has been working in the foundations of the field for over a decade and this volume is a compact version of her doctoral thesis. It includes some of her work in algebraic semantics of general rough sets including those arising from generalized transitive relations, knowledge interpretation and related semantics, and axiomatic approach to granularity, contamination problems and related measures.