I - MATHEMATICS AND PHYSICS

Mean, variance, moments of a distribution
Binomial distribution, Poisson distribution, and Gaussian distribution
Least-squares method
Taylor series
Fourier series and transform
Fundamental laws of Nature
Physical quantities and units
Kinetic energy, potential energy, thermal energy
Angular momentum, orbital angular momentum, spin angular momentum
Laws of thermodynamics
Phase space
Virial theorem
Gravitational field, electromagnetic field
Maxwell's equations
Thomson and Compton scattering, synchrotron radiation, free-free absorption
Blackbody radiation, Planck function
Radiation pressure
Reflection, refraction, interference, diffraction, aberrations
Conduction, convection, radiation, diffusion
Heisenberg's principle
Bohr model of the atom
Laser emission, maser emission
Space and time in Galilean, Special and General Relativity
Time dilation and Lorentz contraction in Special Relativity
Classical and relativistic Doppler shift
Aberration of the light
Equivalence principle

II - ASTRONOMY

Magnitudes and colours
Photometric systems
Surface brightness
Isophotes, isophotal radii
Parallax
Distance modulus
Cosmic distance scale
Redshift
Jeans criterion
Eddington limit
Fundamental and Local Standard of Rest
Solar motion, Solar apex
Stellar proper motions and radial velocities
Velocity ellipsoid
Differential rotation of the Milky Way, Oort constants
Core and tidal radius of a stellar cluster
Classification and physical interpretation of stellar spectra
Stellar opacity, formation of spectral lines and continuum
Emission and absorption spectral lines
Molecular spectral lines
21-cm spectral line
Pressure, temperature, and gravity in stellar atmospheres
Extinction, reddening
Gravitational lensing
X-ray, ultraviolet, optical, infrared, and radio telescopes
Astronomical instrumentation

III - THE SOLAR SYSTEM AND EXTRASOLAR PLANETS

Albedo
Kepler's laws
Two-body problem
Physical properties of the Sun and Solar System
Roche model, Lagrangian points
Oort cloud, Kuiper belt
Escape velocity in planet atmospheres
Detection of extrasolar planets

IV - STARS AND STELLAR POPULATIONS

Perfect gas, degenerate gas
Stefan's law, Wien's law
Botzmann's law, Saha's law
Color temperature
Thermonuclear reactions: proton-proton chain, CNO cycle, triple alpha reaction
Initial mass function
Stellar populations
Globular clusters, open clusters
Stability of the stars: radiative and convective transfer
Stellar evolution, isochrones
Hayashi line
Properties of the colour-magnitude diagram
Properties of the stars on the main sequence
RR Lyrae, cepheids, planetary nebulae
Chandrasekar mass, white dwarfs
Oppenheimer-Volkoff mass, neutron stars, black holes
The Milky Way: components

V - THE INTERSTELLAR MEDIUM

Components of the ISM
Supernovae and SNRs
Molecular clouds
Star formation
Spiral structure in galaxies
Magnetic field in the ISM
Heating and cooling in the ISM

VII - GALAXY CLUSTERS AND COSMOLOGY

Properties and classification of galaxy clusters
Galaxies, dark matter, and gas in galaxy clusters
Free-fall time
Galaxy cluster mass
Matter and energy in the Universe
Hubble's law
Cosmic microwave background
Cosmological principle, Robertson-Walker metric
Standard Friedmann's models of the Universe
Universe models with non-zero cosmological constant
Cosmological parameters
Cosmological horizon, event horizon
Thermal history of the Universe
Nucleosynthesis in the early Universe
Inflation
Correlation functions, spectrum of initial fluctuations
Fluctuations in the cosmic microwave background radiation
Sunyaev-Zeldovich effect