Virtual and Augmented Reality (VR AR) : Foundations and Methods of Extended Realities (XR) This comprehensive textbook offers a scientifically sound and at the same time practical introduction to Virtual and Augmented Reality (VR AR). Readers will gain the theoretical foundation needed to design implement or enhance VR AR systems evaluate and improve user interfaces and applications using VR AR methods assess and enrich user experiences and develop a deeper understanding of how to apply VR AR techniques. Whether utilizing the book for a principal course of study or reference reading students of computer science education media natural sciences engineering and other subject areas can benefit from its in depth content and vivid explanation. The modular structure allows selective sequencing of topics to the requirements of each teaching unit and provides an easy to use format from which to choose specific themes for individual self study. Instructors are provided with extensive materials for creating courses as well as a foundational text upon which to build their advanced topics. The book enables users from both research and industry to deal with the subject in detail so they can properly assess the extent and benefits of VR AR deployment and determine required resources. Technology enthusiasts and professionals can learn about the current status quo in the field of VR AR and interested newcomers can gain insight into this fascinating world. Grounded on a solid scientific foundation this textbook addresses topics such as perceptual aspects of VR AR input and output devices including tracking interactions in virtual worlds real time aspects of VR AR systems and the authoring of VR AR applications in addition to providing a broad collection of case studies. 1 R. Doerner et al. Introduction to Virtual and Augmented Reality 2 R. Doerner and F. Steinicke Perceptual Aspects of VR 3 B. Jung and A. Vitzhum Virtual Worlds 4 P. Grimm at al. VR AR Input Devices and Tracking 5 W. Broll et al. VR AR Output Devices 6 R. Doerner et al. Interaction in Virtual Worlds 7 M. Buhr et al. Real time Aspects of VR Systems 8 W. Broll Augmented Reality 9 R. Doerner et al. VR AR Case Studies 10 W. Broll et al. Authoring of VR AR Applications 11 R. Doerner Mathematical Foundations of VR AR.