The subject of Quantum Cosmology is concerned with providing a quantum mechanical description of the universe as a whole and, within that description, to constructing a theory of the universe's initial condition whose predictions can be compared with observation. The recent progress in this area has profound implications for physics at all scales. The lectures at this School describe these theories and their implications. They cover basic quantum mechanics of cosmology, proposals for theories of initial conditions, and their application to the prediction of the large scale features of our universe. A special emphasis of the School is the implication of topological fluctuations of spacetime (wormholes, baby universes) for the observed coupling constants of the low energy interactions of elementary particles and as a potential explanation for the vanishing of the cosmological constant.