A clear and accessible introduction to quantum mechanical methods used to calculate properties of atoms exposed to strong magnetic fields in both laboratory and stellar environments, with the emphasis on hydrogen and helium and their isoelectronic sequences. The results of the detailed calculations are listed in tables, making it a useful handbook for astrophysicists and atomic physicists alike.

1. Introduction.- 1.1 Magnetic Fields of Compact Cosmic Objects.- 1.2 Historical Review.- 1.3 Notations and Abbreviations.- 2. Interacting Charged Particles in Uniform Magnetic Fields.- 2.1 The N-Body Problem.- 2.2 The Uncharged Two-Body Problem.- 2.3 Scaling Properties of the Coulomb Problem.- 3. Methods of Solution for the Magnetized Coulomb Problem.- 3.1 General Considerations.- 3.2 Numerical Treatment.- 4. Results for Low-Lying States.- 4.1 Energy Values.- 4.2 Wavelengths of the Hydrogen Atom.- 4.3 Wave Functions of the Hydrogen Atom.- 5. Energies for Arbitrarily Excited States in Adiabatic Approximation.- 5.1 Asymptotic Property of the Effective Potentials.- 5.2 Numerical Results and Their Accuracy.- 6. Electromagnetic Transition Probabilities.- 6.1 The General Expressions.- 6.2 Effects of the Finite Proton Mass on the Transition Matrix Element.- 6.3 Results.- 6.4 Expressions for Electromagnetic Transitions in Adiabatic Approximation.- 7. Stationary Lines and White Dwarf Spectra.- 7.1 Stationary Lines.- 7.2 Spectra of Selected Magnetic White Dwarfs.- 7.3 Table of Magnetic White Dwarfs.- 7.4 Future Work.- 8. Relativistic Effects, Nuclear Mass Effects, and Landau-Excited States.- 8.1 Spin-Orbit Coupling.- 8.2 Effects of the Finite Proton Mass and of Motion Perpendicular to the Magnetic Field.- 8.3 Landau-Excited States.- 9. Helium-Like Atoms in Magnetic Fields of Arbitrary Strengths.- 9.1 Correspondence Diagrams.- 9.2 Method of Solution.- 9.3 Dipole Strengths, Oscillator Strengths, and Transition Probabilities.- 9.4 Results for the Two-Electron Problem.- 10. Highly Excited States.- 10.1 Results.- 10.2 Is There Chaos in Quantum Mechanics?.- Outlook.- A1. Energy Values.- A1.1 Tables of the Energy Values.- A1.2 Figures of the Energy Values.- A2. Wavelengths.- A2.1 Figures of the Wavelengths.- A2.2 Tables of Stationary Wavelengths.- A2.3 Figures of Stationary Wavelengths.- A3. Electromagnetic Transition Probabilities.- A3.1 Wavelengths, Dipole Strengths, Oscillator Strengths, and Transition Rates.- A3.2 Oscillator Strengths and Transition Probabilities in Adiabatic Approximation.- A3.3 Dipole Strengths of Stationary Transitions.- A4. Helium and Helium-Like Atoms.- A4.1 Tables of the Energy Values.- A4.2 Wavelengths, Dipole Strengths, Oscillator Strengths, and Transition Rates.- References.