  Spatial branching processes became increasingly popular in the past decades,
not only because of their obvious connection to biology, but also because
superprocesses are intimately related to nonlinear partial differential
equations. Another hot topic in today's research in probability theory is
`random media', including the now classical problems on `Brownian motion among
obstacles' and the more recent `random walks in random environment' and
`catalytic branching' models. These notes aim to give a gentle introduction
into some topics in spatial branching processes and superprocesses in
deterministic environments (sections 2-6) and in random media (sections 7-11).
