This book presents lectures given during a school and workshop organized at Heriot-Watt University in July and August 2006, with funding from the London Mathematical Society (LMS), which supported the Invited Lectures of Michael Singer, and the International Centre for Mathematical Sciences (ICMS) in Edinburgh, which supported the Workshop.

The origin of these events lies in a suggestion made by one of us (AVM) to the other that we should make a proposal for an Isaac Newton Institute programme. After some thought we concluded that a smaller scale proposal would be more appropriate to the present state of the field and the wishes of likely participants, as well as our capacity to write proposals.

We therefore, with his agreement, proposed Michael Singer as the speaker for the 2006 LMS Invited Lecture series, and simultaneously make a proposal to ICMS for a workshop to follow the Invited Lectures: happily both proposals were accepted. We were very glad that in making the workshop proposal we had the assistance of Michael himself and of Sergei Tsarev, who were very helpful in suggesting topics for inclusion and people to invite, whether or not they became speakers.

Between the initial proposal and carrying it out we were fortunate to recruit Chris Eilbeck of Heriot-Watt as an additional organizer. His local knowledge and connections with ICMS were invaluable in actually mounting the event, and it is hard to express our thanks forcefully enough!

Michael Singer is an excellent lecturer of great clarity: from personal experience we also knew that he is generous with his time and ideas, especially to new workers in the field.