This book provides a comprehensive overview and introduces the basic theoretical concepts relevant for modern astrophysics. The book is structured in a modular way and can also be used by other researchers who want to refresh their memory of theoretical aspects in astrophysics. This book provides a comprehensive overview and introduces the basic theoretical concepts relevant for modern astrophysics. The book is structured in a modular way and can also be used by other researchers who want to refresh their memory of theoretical aspects in astrophysics. 1 Introduction2 Kinetic Theory and Distribution Function2.1 Assumptions 2.2 Boltzmann Equation2.3 Irreversibility and H-Theorem2.4 Equilibrium Distribution Function for Ideal Gases 2.5 Fokker-Planck Approximation 2.6 Moments of the Boltzmann Equation3 Hydrodynamics 3.1 Assumptions and Limitations 3.2 Equations of Hydrodynamics 3.3 The Tensor Virial Theorem 4 Aspects of Classical Hydrodynamics: Flows of Ideal and Viscous Fluids 4.1 Flows of Ideal Fluids 4.2 Flows of Viscous Fluids 5 Sound Waves and Shock Fronts 5.1 Sound Waves in Ideal Fluids 5.2 Examples of Supersonic Flows in Steady State 5.3 Steepening of Sound Waves 5.4 Shock Waves 5.5 The Sedov Solution 6 Fluid Instabilities 6.1 Gravitational Instability 6.2 Rotational Instability 6.3 Rayleigh-Taylor Instability 6.4 Convection 6.5 Kelvin-Helmholtz Instability 6.6 Thermal Instability 6.7 Turbulence 7 Magneto-Hydrodynamics 7.1 Maxwell's Equations and Units 7.2 The Magneto-Hydrodynamic Equations 7.3 Hydro-Magnetic Waves 7.4 Magnetorotational Instability in Accretion Disks7.5 Generation of Magnetic Fields 7.6 Ambipolar Diffusion 8 Concepts of Plasma Physics 8.1 Basic Concepts 8.2 The Dielectric Tensor 8.3 Dispersion Relations 8.4 Waves in a Thermal Plasma 8.5 Waves in Magnetized Cold Plasmas 9 Concepts of Stellar Dynamics 9.1 Time Scales 9.2 Jeans Equation 9.3 The Virial Equations in Stellar Dynamics 9.4 Jeans Theorem 9.5 Distribution Functions for Spherical Systems: Isothermal Sphere 9.6 Equilibrium and Relaxation 9.7 Stability 9.8 The Rigidly Rotating Disk 9.9 Spiral Density Waves and Bars9.10 Dynamical Friction 9.11 Application of the Fokker-Planck Equation to Star Clusters10 Special Relativity 10.1 Four Vectors10.2 Transformation between Inertial Frames10.3 Time Dilation, Lorentz Contraction, and Twin Paradoxon10.4 Short Preview of General Reletivity11 Fundamental Concepts of Radiation 11.1 Basic Quantities 11.2 Transport of Radiation through Matter 11.3 Thermal Radiation 11.4 Einstein Coefficients 11.5 Scattering 11.6 Radiative Transport as Diffusion Problem 11.7 Relativistic Invariant 12 Radiation from Charged Particles 12.1 Radiation of a Slowly Moving Charge 12.2 Beaming of Radiation from a Relativistic Particle 12.3 Scattering off Free Electrons 12.4 Scattering off Bound Charges 12.5 Radiation Drag 12.6 Compton Scattering 12.7 The Kompaneets Equation 12.8 Bremsstrahlung 12.9 Synchrotron Radiation 13 Ionisation, Recombination, and Spectra 13.1 Photo-Ionisation 13.2 Natural Width of Spectral Lines 13.3 Collisional Broadening of Spectral Lines 13.4 Velocity Broadening of Spectral Lines 13.5 Voigt Profile 13.6 Equivalent Width and Curve-of-Growth13.7 Atomic Structure and Selection RulesAppendixA.1 Vector CalculusA.2 Differential Operators in Cylindrical and Spherical Coordinate SystemA.4 Taylor ExpansionA.5 Fourier Series ExpansionA.6 Brief Introduction into Lagrangian and Hamiltonian Dynamics