Recent developments and open problems in linear series

In the week 3--9, October 2010, the Mathematisches Forschungsinstitut at Oberwolfach hosted a mini workshop Linear Series on Algebraic Varieties. These notes contain a variety of interesting problems which motivated the participants prior to the event, and examples, results and further problems which grew out of discussions during and shortly after the workshop. A lot of arguments presented here are scattered in the literature or constitute folklore. It was one of our aims to have a usable and easily accessible collection of examples and results.