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Originally published in 1915, this textbook was written by English mathematician Harry Bateman (1882-1946) and 'is intended as an introduction to some recent developments of Maxwell's electromagnetic theory which are directly connected with the solution of the partial differential equation of wave-motion'. Notably, 'the higher developments of the theory which are based on the dynamical equations of motion are not considered'. Instead the book focuses on an overview of the theory of this vast subject, bringing into view the most recent developments. An extensive knowledge and understanding of mathematics is considered a pre-requisite, as is knowledge on the existing theorems surrounding such study. Interestingly, chapter eight contains some of Bateman's own contributions to the subject. This dynamic and engaging book outlines the theory of electrical and optical wave-motion, summarising the fundamental ideas of the subject and will be of considerable value to scholars of physics.