Oz is a concurrent language providing for functional, object-oriented, and constraint programming. This paper defines Kernel Oz, a semantically complete sublanguage of Oz. It was an important design requirement that Oz be definable by reduction to a lean kernel language. The definition of Kernel Oz introduces three essential abstractions: the Oz universe, the Oz calculus, and the actor model. The Oz universe is a first-order structure defining the values and constraints Oz computes with. The Oz calculus models computation in Oz as rewriting of a class of expressions modulo a structural congruence. The actor model is the informal computation model underlying Oz. It introduces notions like computation spaces, actors, blackboards, and threads.