Supersymmetry and Superfields in Three Euclidean Dimensions

The simplest supersymmetry algebra and superspace in three dimensional Euclidean (3dE) space is examined. Representations of the algebra are considered and the implications of restricting the space of states to states with positive definite norm are determined. A superspace is defined and superfields are introduced. Supersymmetric field theory models in 3dE are described both in superfield and component field forms. The relationship between these models, and similar models in four dimensional Minkowski space is described.