Modern astrophysics is a mature science that has evolved from its early phase of discovery and classification to a physics-oriented discipline focused on finding answers to fundamental problems ranging from cosmology to the origin and diversity of life-sustainable systems in the Universe. For this very reason, progress of modern astrophysics requires access to the electromagnetic spectrum in the broadest energy range. The Ultraviolet is a fundamental energy domain since it is one of the most powerful tools to study plasmas at temperatures in the 3,000-300,000~K range as well as electronic transitions of the most abundant molecules in the Universe. Moreover, the UV radiation field is a powerful astrochemical and photoionizing agent.This book describes the fundamental problems in modern astrophysics that cannot progress without easy and wide-spread access to modern UV instrumentation.