This volume collects lecture notes from talks given in the Appalachian Set Theory workshop series (supported by the National Science Foundation) during the period 2006–2012.

This workshop series grew out of an informal series of expository lectures held at Carnegie Mellon University and attended by set theorists from universities in Appalachian states before 2006. The success of these earlier gatherings inspired the editors to formalize the series and seek funding to help more people attend. Participants from other universities were invited to host workshops as well. Typically there are three meetings a year with one taking place at Carnegie Mellon University and the remaining two elsewhere. Several of the workshops have been held in neighbouring regions but the series retains its Appalachian flavour.

At each workshop a leading researcher lectures for six hours on an important topic or technique in modern set theory. Students are engaged to assist in writing notes based on the lectures, and these notes are disseminated on the web. This provides a learning opportunity for the students and makes the notes universally available.

The papers collected here represent more polished versions of the lecture notes from most of the workshops to date. They were prepared collaboratively by the lecturers and the student assistants. The lecturers are the principal authors and their names appear first, followed by the names of the assistants. One workshop (represented in Chapter 7) had two lecturers, and two workshops (represented in Chapters 1 and 13) had two assistants.