  I survey physics theories involving parallel universes, which form a natural
four-level hierarchy of multiverses allowing progressively greater diversity.
  Level I: A generic prediction of inflation is an infinite ergodic universe,
which contains Hubble volumes realizing all initial conditions - including an
identical copy of you about 10^{10^29} meters away.
  Level II: In chaotic inflation, other thermalized regions may have different
effective physical constants, dimensionality and particle content.
  Level III: In unitary quantum mechanics, other branches of the wavefunction
add nothing qualitatively new, which is ironic given that this level has
historically been the most controversial.
  Level IV: Other mathematical structures give different fundamental equations
of physics. The key question is not whether parallel universes exist (Level I
is the uncontroversial cosmological concordance model), but how many levels
there are. I discuss how multiverse models can be falsified and argue that
there is a severe "measure problem" that must be solved to make testable
predictions at levels II-IV.
