In the last few years there has been a revival of interest in the old idea that spacetime may have more than four dimensions, all but four having been curled up into a small circumference. In this view the various particles and interactions we see at ordinary energies arise from a simple, perhaps purely geometrical, theory in higher dimensions. This idea has profound implications for elementary particle physics and cosmology, and raises challenging problems of mathematics. These matters were the topic of the Second Jerusalem Winter School of Theoretical Physics.

The School explored the delicate interplay between geometry and statistical mechanics in these materials such as microemulsions, wetting and growth interfaces, bulk lyotropic liquid crystals, chalcogenide glasses and sheet polymers, using tools from the fields of polymer physics, of differential geometry and of critical phenomena.

We read in order to know we are not alone, I once heard, and perhaps it could also be suggested that we write in order not to be alone, to endorse, to promote continuity. The idea for this book took about ten years to materialize, and it is the author’s hope that its content will constitute the beginning of further explorations beyond current horizons. More speci cally, this book appeals to the reader to engage upon and persevere with a journey, moving through the less well explored territories in the evolution of the very early universe, and pushing towards new landscapes. P- haps, during or after consulting this book, this attitude and this willingness will be embraced by someone, somewhere, and this person will go on to enrich our quantum cosmological description of the early universe, by means of a clearer supersymm- ric perspective. It is to these creative and inquisitive ‘young minds’ that the book is addressed. The reader will not therefore nd in this book all the answers to all the problems regarding a supersymmetric and quantum description of the early universe, and this remark is substantiated in the book by a list of unresolved and challenging problems, itself incomplete.