the space of theories we can absorb the scales $\Lambda$, $\bar\Lambda$, $\mu$ into the definitions of the operators, thus making the scale matching relation  seem trivial. The non-trivial content in  is its consistency with duality under all possible deformations of both theories. Indeed, we will see that consistency leads to highly non-trivial checks of duality. The situation is reminiscent of the Zamolodchikov metric in two dimensional field theory, which is trivial at any given point in the space of theories, but whose curvature carries invariant geometrical information. The scale matching also describes an invariant relation between the geometries of the spaces of electric and magnetic theories.

We plan to discuss two main issues. The first is the structure of the quantum chiral ring and moduli space, and their transformation under duality. The second is non-trivial quantitative tests of duality, which are possible because of the large number of vacua that the system possesses in general. In all these tests one uses symmetries to write down certain duality relations. This leaves in general some undetermined functions of the coupling constants. These functions can be calculated by assuming duality in some vacua of the theory. Since there are in general many more 