  In the main part of this PhD thesis, we consider a periodically realized
microscopic superconductor described by BCS theory, which is subject to
external electromagnetic fields. We show that the superconductor is properly
described by Ginzburg--Landau theory in the macroscopic and weak magnetic field
limit. The main novelty of our results is to allow for a non-vanishing magnetic
flux through the unit cell of the lattice of periodicity. These main results
are supplemented by various unpublished notes in the field of BCS theory.
Furthermore, we preface the presentation of these results with a comprehensive
introduction suitable for master's or PhD students. Thereby, we hope to
contribute to filling the gap of missing introductory literature in the field.
  The thesis comprises a second topic, in which we provide ideas for setting up
quantum lattice systems in order to prove exponential estimates for the
adiabatic theorem. These notes are the result of studies in this field, which
have been conducted during a research stay at the University of British
Columbia (UBC) in Vancouver, Canada.
