  The Everett interpretation of quantum mechanics divides naturally into two
parts: first, the interpretation of the structure of the quantum state, in
terms of branching, and second, the interpretation of this branching structure
in terms of probability. This is the first of two reviews of the Everett
interpretation, and focuses on structure, with particular attention to the role
of decoherence theory. Written in terms of the quantum histories formalism,
decoherence theory just is the theory of branching structure, in Everett's
sense.
