(plenary invited speaker)

Singularities in classical and quantum cosmology

We consider some cosmological models where soft future singularities arise and discuss how the crossing of these singularities can change the properties of matter fields. We also compare different approaches to the possibility of the crossing of the singularities of the Big Bang – Big Crunch type. We discuss what happens with the singularities in quantum cosmology and study what happens with the quantum particles when a universe crosses a singularity. We briefly review recent attempts to develop a general approach studying the singularities in the functional space.