This book aims to discuss recent achievements in the field of electromagnetic theory. The book includes 7 chapters from various branches of physics, starting from the standard paradigm of Maxwell’s equations and ending with penetration into the world of elementary particles and the union with gravity. In particular, chapters present: a recently discovered theorem in integral vector calculus, actually a theorem and a corollary, aimed at advancing our understanding and analysis of electromagnetic phenomena;the possibility of revisiting the capacitor charging problem; a non-monochromatic consideration of the electromagnetic phenomena, though electrodynamics courses and textbooks usually consider solutions based on a monochromatic plane wave;electromagnetism and gravity with a focus on antigravity; a combination of the gravitational force with the electrostatic force at the Planck scale; problematic fundamental issues in the electromagnetic theory; and dramatic conceptual problems of the electroweak theory of the Standard Model of particle physics Thus, the general picture of the book, organized in the form of a set of chapters, is an emphasis on novelty and new mathematics, new types of solutions, new problems, new applications, finding a connection with gravity, clarifying the fundamental problems of the theory elementary particles and, finally, the derivation of Maxwell’s equations that include both an electric charge and a magnetic monopole.