We will give a brief introduction to the theory of quasi-conformal mappings, both in the plane and in higher dimensions. We will discuss the connections between the theory of QC maps and other branches of mathematics, the major tools and methods used in the study, and the development of some important problems. Furthermore, we will devote to the discussion of two conformal invariants - modulus and capacity, which are indispensable tools in the study of quasiconformal mappings. The concept of QED (for quasi-extremal distance) domains will be introduced. This class of domains play an important role in the study of QC maps and geometric function theory. In this lecture an important geometric and topological characterization will be given for domains with QED constant M(D) = 2. The values of the QED constants will be computed for some special domains such as polygons and cubes.