With increased pressure to reduce costs associated with design, fabrication, and launch of space structures, there has been a resurgence in interest for membrane structures for extraterrestrial use. Applications for membrane and inflatable structures in space include lunar and planetary habitats, radio frequency reflectors and wave guides, optical and infrared imaging, solar concentrators for solar power and propulsion, sun shades, solar sails, and may others. The text begins with a broad overview and historical review of the technologies, proceeds to theoretical discussion of the mechanics and physics, ad then proceeds into current applications and case studies.