This book shows that some unexplained cosmological and electrodynamic phenomena may be treated and understood in the geometrically based framework of Weyl and Dirac. After a short introductory chapter, Chapters 2 and 3 consider the Weyl-Dirac space-time as a geometric basis appropriate for building up relativistic theories. In the following chapter the Weyl-Dirac unified theory of gravitation and eletromagnetism, as well as its consequences, are discussed. Chapter 5 presents a modified version of the original Weyl-Dirac theory. In Chapter 6 the Weyl-Dirac theory enriched by Rosen's approach is considered as a source of geometrically based dark matter. Chapter 7 gives an integrable version of Weyl-Dirac theory, in which matter is created by geometry. In Chapter 8 an outlook of the Weyl-Dirac framework is given and its applicability to extended theories of electromagnetism, and cosmology is discussed.