Quantum cosmology is the quantum theory of the entire universe. Although
strange at first sight, it is appropriate because (1) our world appears to be
fundamentally quantum, (2) the classical description of gravity breaks down at
singularities it would give at the beginning of the universe, and (3) our
universe has many properties that cannot be explained by a classical
description of them. A quantum state of the universe should obey certain
constraints, such as the Wheeler-DeWitt equations. One approach to interpreting
such a state is {\it Sensible Quantum Mechanics} (SQM), in which nothing is
probabilistic, except, in a certain frequency sense, conscious perceptions.
Sets of these perceptions can be deterministically realized with measures given
by expectation values of positive-operator-valued {\it awareness operators}.
These may be defined even when the quantum state itself is not normalizable,
though there still seem to be problems of divergences when one has an infinite
amount of inflation, producing infinitely large spatial volumes with presumably
infinite measures of perceptions. Ratios of the measures for sets of
perceptions (if finite) can be interpreted as frequency-type probabilities for
many actually existing sets rather than as propensities for potentialities to
be actualized, so there is nothing indeterministic in a specific SQM. One can
do a Bayesian analysis to test between different specific SQMs. One can also
make statistical predictions of what one might perceive within a specific SQM
by invoking the {\it Conditional Aesthemic Principle}: among the set of all
conscious perceptions, our perceptions are likely to be typical.Comment: LaTeX, 18 pages, lectures at the First Mexican School on Gravitation
and Mathematical Physics, December 12-16, 199
