This book is on the celebrated topic of rational billiards, translation surfaces and their fractal analogs. It contains a gentle introduction to Complec analysis and Complex geometry on Riemann surfaces. The book also touches on the topic of moduli spaces of translation surfaces and the SL2R action thereon. The author then discusses his own research in fractal billiards. This book is suitable for advanced undergraduates and beginning graduate students looking to get into the field of rational billiards and translations surfaces (and their generalizations, e.g., flows on moduli spaces of translation surfaces).

Author Biography

Robert G. Niemeyer is an assistant professor in the Department of Mathematics & Statistics at the University of Maine in Orono, ME and a member of CompuMAINE. As part of the UMaine Department of Mathematics and Statistics, he is actively engaged in research, teaching and mentoring undergraduate and graduate students. He is a dynamicist with specific research interests in topological dynamical systems, both pure and applied.