Cooper pairing of fermions is a profound phenomenon that has become very important in many different areas of physics in the recent past. This book brings together, for the first time, experts from various fields involving Cooper pairing, at the level of BCS theory and beyond, including the study of novel states of matter such as ultracold atomic gases, nuclear systems at the extreme, quark matter and application to compact stars. Cross-disciplinary in nature, the book will be of interest to physicists in many different specialties, including condensed matter, nuclear, high-energy, and astrophysics. The emphasis is on novel issues beyond ordinary BCS theory such as pairing in asymmetric systems, the polarization effect, and higher spin pairing. These topics are rarely treated at the textbook level and all of them are the subjects of intensive ongoing research. The book also considers various new techniques -- for example, finite temperature field theory -- widely used in current research that differ significantly from the conventional condensed matter approaches described in the standard literature.