  An overview is given in section 1, of uncertain building blocks of
present-day cosmologies. Thereafter, these edited lecture notes deal with the
following four special problems: (1) They advertise Wiltshire's result --
making `dark energy' obsolete -- that accelerated cosmic expansion may be an
artefact, due to an incorrect evaluation of the cosmic timescale in a Universe
whose bulk matter is inhomogeneously distributed. (2) They cast doubt on
Hawking's prediction of black-hole evaporation. (3) They point at various
inconsistencies of the black-hole paradigm, in favour of nuclear-burning
central engines of AGN. (4) They re-interpret (a best case of) `anomalous
redshifts' as non-cosmological, kinematic redshifts in strong jet sources.
