Agradecimentos: To the undergraduate and graduate students who followed our courses on Weber's Electrodynamics for the many constructive remarks they presented. To our students who are developing researches in this area. To all those who read a first version of this work and gave their feedback. To Drs. Peter and Neal Graneau, Thomas E. Phipps Jr., James Paul Wesley, Domina E. Spencer, Julian B. Barbour, Harvey R. Brown, C. Roy Keys, Svetlana Tolchelnikova, Amitabha Ghosh, Umberto Bartocci, Roberto Monti, Cesar Lattes, Roberto de A. Martins, Roberto A. Clemente, Marcio Menon, Marcos C. D. Neves, Werner M. Vieira, Waldyr A. Rodrigues Jr., Ibere L. Caldas, Alvaro Vannucci, Haroldo C. Velho and to all those who helped us with their ideas and suggestions. To all our friends who were kind enough to listen patiently to the names Weber and Mach so many times... In particular we wish to thank FAPESP, CNPq and FAEP (Brazil) for financial support during the last years. To the Center for Electromagnetics Research, Northeastern University (Boston, USA), which received us for one year in which part of this work was written. Also to the Institutes of Physics and Mathematics of the State University of Campinas - UNICAMP (Brazil), that gave all the necessary support to undertake this work. Finally I wish to thank my parents, my wife and children for the stimulus they always Ver menos