The aim of the present book is very simply stated; it is to discuss - and to some extent to explore - the Weyl-Dirac theory in connection with classical electromagnetism and cosmology. The study of our universe in recent years has become one of the most interesting and important subjects. Current cosmology considers a large number of various subjects from elementary particles to the large scale-structure of the universe. In order to explain this variety of phenomena, which occur between the Planck time and tens of billions of years, one makes use of methods stemming from different physical theories: elementary particle physics, quantum mechanics, thermodynamics, statistical physics, celestial mechanics, etc. It is, however, generally accepted to express those approaches in terms of the general theory of relativity, which is based on Riemann's geometry. In this book, it is shown that some unexplained cosmological and electrodynamic phenomena may be treated and understood in the geometrically based framework of Weyl and Dirac.The book is intended for physicists, astrophysicists, cosmologists and mathematicians who are familiar with the foundations of Einstein's general theory of relativity.