It is becoming increasingly clear that our modern technological society is vulnerable to the impacts of severe solar storms, as well as radiation, particle and geomagnetic disturbances. However, the potential severity of these extreme solar events and their probability of occurring are unknown. What can we expect from the Sun? What could the most severe solar particle storms look like? Does the Sun have an unlimited ability to produce severe storms? Can a destructive "black swan" event occur? Direct solar data covers only several decades, a period too short to answer these questions. Fortunately, other indirect ways to study these, possibly rare, extreme solar storms have been discovered, paving the way for analysis of these events on the multi-millennial timescale. At present, studies of extreme solar events are growing, forming a new research discipline. This book, written by leaders in the corresponding aspects of the field, presents a first systematic review of the current state of the art.