Prologue.- I Quanta and Molecules: The Quantum Theory of Planck, Einstein and Nernst.- 1.1 The Law of Blackbody Radiation.- 1.2 The Significance of the Constants in Planck's Law.- 1.3 Fluctuations and Light-Quanta.- 1.4 Energy-Quanta and the Derivations from Classical Theories.- 1.5 The Search for Other Quantum Phenomena.- 1.6 Specific Heats, New Quantum Hypotheses and the First Solvay Conference.- 1.7 The Consolidation of Quantum Theory.- II The Bohr-Sommerfeld Theory of Atomic Structure.- II.1 The Spectra of Atoms and Molecules: The Empirical Foundations.- II.2 Ideas Towards a Model of Atomic Structure.- II.3 Niels Bohr and the Origin of the Quantum Theory of Line Spectra.- II.4 Atoms as Conditionally Periodic Quantum Systems.- II.5 Three Principles of Atomic Theory.- III The Bohr Festival in Göttingen.- III.1 The Gottingen Tradition of Mathematics and Physics.- III.2 The Continuity of the Tradition: Richard Courant, Max Born and James Franck in Gottingen.- III.3 Progress in Atomic Models from 1913 to 1921.- III.4 Bohr's Wolfskehl Lectures and the Theory of the Periodic System of Elements.- III.5 Immediate Impact and Triumph of Bohr's Theory of the Periodic System of Elements.- IV The Mechanical and Spectroscopic Failures of Atomic Models.- IV. 1 Wolfgang Pauli's Background and Early Scientific Work.- IV.2 The Helium Atom and Other Few-Body Problems.- IV.3 The Magnetic Anomaly and the Stern-Gerlach Effect.- IV.4 The Anomalous Zeeman Effect.- IV. 5 The Breakdown of the Bohr-Sommerfeld Theory: Anomalous Zeeman Effects and the Crossed-Field Problem.- V The Problems of Radiation Theory.- V.1 The Proof of the Light-Quantum Hypothesis.- V.2 The Bohr-Kramers-Slater Theory of Radiation.- V.3 Bose's Light-Quantum Statistics and Its Extension to Gas Theory.- V.4 The Phase Waves Associated with Matter.- V. 5 The Status of the Radiation Problem in 1925.- VI New Methods and Concepts in Atomic Theory.- VI.1 The Dispersion-Theoretic Approach.- VI.2 Atomic Structure and the Problem of Closed Electron Shells.- VI.3 The Rule for Equivalent Electrons: Pauli's Exclusion Principle.- VI.4 The Discovery of Electron Spin.- Epilogue.- References.- Author Index.