Note: Intro -- Solar and Stellar Dynamos -- Preface -- Acknowledgments -- Contents -- List of Previous Saas-Fee Advanced Courses -- 1 Magnetohydrodynamics -- 1.1 The Fluid Approximation -- 1.1.1 Matter as a Continuum -- 1.1.2 Solid Versus Fluid -- 1.2 Essentials of Hydrodynamics -- 1.2.1 Mass: The Continuity Equation -- 1.2.2 The D/Dt Operator -- 1.2.3 Linear Momentum: The Navier--Stokes Equations -- 1.2.4 Angular Momentum: The Vorticity Equation -- 1.2.5 Energy: The Entropy Equation -- 1.3 The Magnetohydrodynamical Induction Equation -- 1.4 Scaling Analysis -- 1.5 The Lorentz Force -- 1.6 Joule Heating -- 1.7 The Full Set of MHD Equations -- 1.8 MHD Waves -- 1.9 Magnetic Energy -- 1.10 Magnetic Flux Freezing and Alfvén's Theorem -- 1.11 The Magnetic Vector Potential -- 1.12 Magnetic Helicity -- 1.13 Force-Free Magnetic Fields -- 1.14 The Ultimate Origin of Astrophysical Magnetic Fields -- 1.14.1 Why B and not E ? -- 1.14.2 Monopoles and Batteries -- 1.15 The Astrophysical Dynamo Problem(s) -- 1.15.1 A Simple Dynamo -- 1.15.2 The Challenges -- Bibliography -- 2 Decay and Amplification of Magnetic Fields -- 2.1 Resistive Decays of Magnetic Fields -- 2.1.1 Axisymmetric Magnetic Fields -- 2.1.2 Poloidal Field Decay -- 2.1.3 Toroidal Field Decay -- 2.1.4 Results for a Magnetic Diffusivity Varying with Depth -- 2.1.5 Fossil Stellar Magnetic Fields -- 2.2 Magnetic Field Amplification by Stretching and Shearing -- 2.2.1 Hydrodynamical Stretching and Field Amplification -- 2.2.2 The Vainshtein & -- Zeldovich Flux Rope Dynamo -- 2.2.3 Hydrodynamical Shearing and Field Amplification -- 2.2.4 Toroidal Field Production by Differential Rotation -- 2.3 Magnetic Field Evolution in a Cellular Flow -- 2.3.1 A Cellular Flow Solution -- 2.3.2 Flux Expulsion -- 2.3.3 Digression: The Electromagnetic Skin Depth -- 2.3.4 Timescales for Field Amplification and Decay. , 2.3.5 Flux Expulsion in Spherical Geometry: Axisymmetrization -- 2.4 Two Anti-Dynamo Theorems -- 2.4.1 Zeldovich's Theorem -- 2.4.2 Cowling's Theorem -- 2.5 The Roberts Cell Dynamo -- 2.5.1 The Roberts Cell -- 2.5.2 Dynamo Solutions -- 2.5.3 Exponential Stretching and Stagnation Points -- 2.5.4 Mechanism of Field Amplification in the Roberts Cell -- 2.5.5 Fast Versus Slow Dynamos -- 2.6 The CP Flow and Fast Dynamo Action -- 2.6.1 Dynamo Solutions -- 2.6.2 Fast Dynamo Action and Chaotic Trajectories -- 2.6.3 Magnetic Flux Versus Magnetic Energy -- 2.6.4 Fast Dynamo Action in the Nonlinear Regime -- 2.7 Dynamo Action in Turbulent Flows -- Bibliography -- 3 Dynamo Models of the Solar Cycle -- 3.1 The Solar Magnetic Field -- 3.1.1 Sunspots and the Photospheric Magnetic Field -- 3.1.2 Hale's Polarity Laws -- 3.1.3 The Magnetic Cycle -- 3.1.4 Sunspots as Tracers of the Sun's Internal Magnetic Field -- 3.1.5 A Solar Dynamo Shopping List -- 3.2 Mean-Field Dynamo Models -- 3.2.1 Mean-Field Electrodynamics -- 3.2.2 The alpha-Effect -- 3.2.3 Turbulent Pumping -- 3.2.4 The Turbulent Diffusivity -- 3.2.5 The Mean-Field Dynamo Equations -- 3.2.6 Dynamo Waves -- 3.2.7 The Axisymmetric Mean-Field Dynamo Equations -- 3.2.8 Linear alpha-Omega Dynamo Solutions -- 3.2.9 Nonlinearities and alpha-Quenching -- 3.2.10 Kinematic alpha-Omega Models with alpha-Quenching -- 3.2.11 Enters Meridional Circulation: Flux Transport Dynamos -- 3.2.12 Interface Dynamos -- 3.3 Babcock--Leighton Models -- 3.3.1 Sunspot Decay and the Babcock--Leighton Mechanism -- 3.3.2 Axisymmetrization Revisited -- 3.3.3 Dynamo Models Based on the Babcock--Leighton Mechanism -- 3.3.4 The Babcock--Leighton Poloidal Source Term -- 3.3.5 A Sample Solution -- 3.4 Models Based on HD and MHD Instabilities -- 3.4.1 Models Based on Shear Instabilities -- 3.4.2 Models Based on Flux-Tube Instabilities. , 3.5 Global MHD Simulations -- 3.6 Local MHD Simulations -- Bibliography -- 4 Fluctuations, Intermittency and Predictivity -- 4.1 Observed Patterns of Solar Cycle Variations -- 4.1.1 Pre-Telescopic and Early Telescopic Sunspot Observations -- 4.1.2 The Sunspot Cycle -- 4.1.3 The Butterfly Diagram -- 4.1.4 The Waldmeier and Gnevyshev--Ohl Rules -- 4.1.5 The Magnetic Activity Cycle -- 4.1.6 The Maunder Minimum -- 4.1.7 From Large-Scale Magnetic Fields to Sunspot Number -- 4.2 Cycle Modulation Through Stochastic Forcing -- 4.3 Cycle Modulation Through the Lorentz Force -- 4.4 Cycle Modulation Through Time Delays -- 4.5 Intermittency -- 4.6 Model-Based Cycle Predictions -- 4.6.1 The Solar Polar Magnetic Field as a Precursor -- 4.6.2 Model-Based Prediction Using Solar Data -- Bibliography -- 5 Stellar Dynamos -- 5.1 Early-Type Stars -- 5.1.1 Mean-Field Models -- 5.1.2 Numerical Simulations of Core Dynamo Action -- 5.1.3 Getting the Magnetic Field to the Surface -- 5.1.4 Alternative to Core Dynamo Action -- 5.2 A-Type Stars -- 5.2.1 Observational Overview -- 5.2.2 The Fossil Field Hypothesis -- 5.2.3 Dynamical Stability of Large-Scale Magnetic Fields -- 5.2.4 The Transition to Solar-Like Dynamo Activity -- 5.3 Solar-Type Stars -- 5.3.1 Observational Overview -- 5.3.2 Empirical Stellar Activity Relationships -- 5.3.3 Solar and Stellar Spin-Down -- 5.3.4 Modelling Dynamo Action in Solar-Type Stars -- 5.4 Fully Convective Stars -- 5.5 Pre- and Post-Main-Sequence Stars -- 5.6 Compact Objects -- 5.7 Galaxies and Beyond -- Bibliography -- Appendix A Useful Identities and Theorems from Vector Calculus -- A.1 Vector Identities -- A.2 The Gradient Theorem -- A.3 The Divergence Theorem -- A.4 Stokes' Theorem -- A.5 Green's Identities -- Appendix B Coordinate Systems and the Fluid Equations -- B.1 Cylindrical Coordinates (s,φ,z). , B.1.1 Conversion to Cartesian Coordinates -- B.1.2 Infinitesimals -- B.1.3 Vector Operators -- B.1.4 The Divergence of a Second-Order Tensor -- B.1.5 Components of the Viscous Stress Tensor -- B.1.6 Equations of Motion -- B.1.7 The Energy Equation -- B.1.8 The MHD Induction Equation -- B.2 Spherical Coordinates (r,θ,φ) -- B.2.1 Conversion to Cartesian Coordinates -- B.2.2 Infinitesimals -- B.2.3 Vector Operators -- B.2.4 The Divergence of a Second-Order Tensor -- B.2.5 Components of the Viscous Stress Tensor -- B.2.6 Equations of Motion -- B.2.7 The Energy Equation -- B.2.8 The MHD Induction Equation -- Appendix C Physical and Astronomical Constants -- C.1 Physical Constants -- C.2 Astronomical Constants -- Appendix D Maxwell's Equations and Physical Units -- D.1 Maxwell's Equations -- D.2 Conversion of Units -- Index.