The emphasis in this text is on classical electromagnetic theory and electrodynamics, that is, dynamical solutions to the Lorentz-force and Maxwell's equations. Numerous worked examples and exercises dispersed throughout the text help the reader understand new concepts and facilitate self-study of the material. Each chapter concludes with a set of problems, many with answers. Complete solutions are also available, as are a number of Maple worksheets to facilitate difficult calculations. This text is designed for upper-level undergraduate and beginning graduate courses in physics or mathematical physics. It should also be of interest to practicing physicists and electrical engineers who desire a deeper geometrical appreciation of electrodynamics and want to access powerful new calculational tools for its application. Mathematicians will find an introduction to geometric methods with paravectors in Clifford algebras and their applications in relativistic physics. No prior study is required of relativistic dynamics or Clifford algebras.