Quantum cosmology is the application of quantum theory to the Universe as a whole. At first glance such an attempt seems surprising since one is used to apply quantum theory to microscopic systems. Why, then, does one wish to extrapolate it to the whole Universe? This extrapolation is based on the assumption that quantum theory is universally valid, in particular that there is no a priori classical world. The main motivation for this assumption comes from the kinematical non-locality (or non-separability) of quantum theory, i.e., from the fact that one cannot in general assign a wave function to a given system since it is not isolated but coupled to its natural environment, which is again coupled to another environment, and so forth. The extrapolation of this quantum entanglement thus leads inevitably to the concept of a wave function for the Universe. Many experiments, notably those which contradict Bell's inequalities, have impressively demonstrated this fundamental non-separability of quantum theory. As we will see in Sect. 3, it is this entanglement between many degrees of freedom which is also responsible for the emergence of a classical world. The importance of this effect seems to have been overlooked in the traditional discussion of quantum theory, and led to the belief in an independently existing classical world.