  We present Voevodsky's construction of a model of univalent type theory in
the category of simplicial sets.
  To this end, we first give a general technique for constructing categorical
models of dependent type theory, using universes to obtain coherence. We then
construct a (weakly) universal Kan fibration, and use it to exhibit a model in
simplicial sets. Lastly, we introduce the Univalence Axiom, in several
equivalent formulations, and show that it holds in our model.
  As a corollary, we conclude that Martin-L\"of type theory with one univalent
universe (formulated in terms of contextual categories) is at least as
consistent as ZFC with two inaccessible cardinals.
