Classification of the N=1 Seiberg-Witten Theories

We present a systematic study of N=1 supersymmetric gauge theories which are in the Coulomb phase. We show how to find all such theories based on a simple gauge group and no tree-level superpotential. We find the low-energy solution for the new theories in terms of a hyperelliptic Seiberg-Witten curve. This work completes the study of all N=1 supersymmetric gauge theories where the Dynkin index of the matter fields equals the index of the adjoint (mu=G), and consequently all theories for which mu<G.