This text is a substantially complete presentation of the electrodynamics developed by Wilhelm Weber. Weber's force between point charges is explored and thoroughly analysed. Ampere's force between current elements is discussed in connection with modern experiments relating to the Ampere versus Grassmann-Biot-Savart controversy. Ampere's force is a central feature of this work, as Maxwell maintained it should always be in the study of electrodynamics, although it is included in few textbooks on electromagnetism. A detailed study of this force is a feature of this book. Other topical questions of physics are analysed, such as a potential-dependent inertial mass, Mach's principle and the origin of inertia, action at a distance as opposed to contact actions, etc. No previous knowledge of the subject is required, and all topics are introduced with both their historical backgrounds as well as modern experimental evidence. This volume will appeal to physicists, mathematicians, electrical and electronic engineers, historians and philosophers of science.