  These notes are a slightly enlarged version of my habilitation thesis, where
our research interest and main results in the past few years are summarized.
Most of the discussion revolves around complex ordinary differential equations
and their underling foliations, singularity theory and dynamical systems.
Compared to the original text, a section containing some background material on
holomorphic foliations was added. Also some new results obtained in the past
three years that are in line with the one presented in the habilitation were
included.
