Topological Foundations of Electromagnetism seeks a fundamental understanding of the dynamics of electromagnetism; and marshals the evidence that in certain precisely defined topological conditions, electromagnetic theory (Maxwell''s theory) must be extended or generalized in order to provide an explanation and understanding of, until now, unusual electromagnetic phenomena. Key to this generalization is an understanding of the circumstances under which the so-called A potential fields have physical effects. Basic to the approach taken is that the topological composition of electromagnetic fields is the fundamental conditioner of the dynamics of these fields. The treatment of electromagnetism from, first, a topological perspective, continuing through group theory and gauge theory, to a differential calculus description is a major thread of the book. Suggestions for potential new technologies based on this new understanding and approach to conditional electromagnetism are also given. Sample Chapter(s). Chapter 1: Electromagnetic Phenomena Not Explained by Maxwell''s Equations260 (437 KB). Contents: Electromagnetic Phenomena Not Explained by Maxwell''s Equations; The Sagnac Effect: A Consequence of Conservation of Action Due to Gauge Field Global Conformal Invariance in a Multiply Joined Topology of Coherent Fields; Topological Approaches to Electromagnetism. Readership: Physicists; advanced undergraduate and graduate students in physics; electrical engineers.