Abstract: The lecture summarizes the habilitation thesis of the author presented at
the University of Ostrava. It is based on a series of papers covering work from the period
2007-2015 on spectral properties of Schroedinger operators: these are problems which deal with
spectral analysis of the Schroedinger operators with the potentials unbounded from below
exhibiting spectral transitions, the operators defined on geometrically nontrivial regions,
the magnetic Laplacians in three dimensional magnetic bottles, and periodic quantum
graphs with gaps in the spectrum.
