讲座内容：

Motivated by the famous Szekeres-Seymour Cycle Double Cover Conjecture and recent advances in hamiltonian cycle enumeration problems in planar graphs, in this lecture series we investigate the interplay between hamiltonian cycles and cycle double covers. We will begin with a short chapter covering basic definitions and some useful auxiliary tools. Most of the results we aim at rely in some way on planarity, so in the second chapter we discuss planar graphs. In the third chapter we then present selected results on hamiltonicity, with a special focus on hamiltonian cycles in planar graphs. In the final chapter we speak about cycle double covers and their connection to hamiltonian cycles, again with a focus on the planar case. This final chapter also contains a series of open research problems.