  These are notes based on a mini-course at the conference RIEMain in Contact,
held in Cagliari, Sardinia, in June 2018. The main theme is the connection
between Reeb dynamics and topology. Topics discussed include traps for Reeb
flows, plugs for Hamiltonian flows, the Weinstein conjecture, Reeb flows with
finite numbers of periodic orbits, and global surfaces of section for Reeb
flows. The emphasis is on methods of construction, e.g. contact cuts and
lifting group actions in Boothby-Wang bundles, that might be useful for other
applications in contact topology.
