In this review article we study the Minimal Supersymmetric Electro-Weak theory (of leptons). The Lagrangian is constructed step by step in great detail, both in the superfield and component field formalism --- both on and off shell. Furthermore the Lagrangian is written in the more familiar four component formalism. Electro weak symmetry breaking is discussed, and the physical chargino- and neutralino states are introduced and discussed.