Magnetic fields are responsible for much of the variability and structuring in the universe, but only on the Sun can the basic magnetic field related processes be explored in detail. While several excellent textbooks have established a diagnostic foundation for exploring the physics of unmagnetized stellar atmospheres through spectral analysis, no corresponding treatise for magnetized stellar atmospheres has been available. The present monograph fills this gap. The theoretical foundation for the diagnostics of stellar magnetism is developed from first principles in a comprehensive way, both within the frameworks of classical physics and quantum field theory, together with a presentation of the various solar applications. This textbook can serve as an introduction to solar and stellar magnetism for astronomers and physicists at the graduate or advanced undergraduate level and will also become a resource book for more senior scientists with a general interest in cosmic magnetic fields.