Principles of Relativity: Overview of Special Relativity – spacetime interval and Lorentz metric – four vectors – Introduction to general relativity (GR) – equivalence principle – notions of curvature – gravitation as a manifestation of the curvature of spacetime – gravitational redshift and clock corrections – orbits in strong gravity, light bending and gravitational lensing – concept of horizon and ergosphere, hydrostatic equilibrium in GR – gravitational radiation.

Classification of galaxies – contents and dimensions – collisionless stellar dynamics – relaxation time, dynamical friction, violent relaxation – galactic potential and orbits – spiral density wave and Lindblad resonance – rotation curves – Tully-Fisher relation – Central Black Holes and fundamental plane relationship – Mass and Luminosity function – Press Schechter formalism – Star formation history and chemical evolution – active galaxies and activity duty cycle – galaxies at high redshift - clusters and groups – evidence of dark matter

Mechanical, Thermal and Nuclear time scales – Hydrostatic equilibrium (Newtonian and Relativistic) – Polytropic Equation of State – Lane Emden Equation – Degenerte matter Equation of State – White Dwafs and Chandrasekhar limit – Virial Theorem - Radiative Equilibrium – Schwarzschild convection criterion – nuclear energy generation – stages of nuclear burning – full set of stellar structure equations – example solutions – HR diagram and the main sequence – Schonberg-Chandrasekhar limit – post- main sequence evolution – Hayashi tracks – Horizontal branch – giant and asymptotic giant branches

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Tutorials on Fitting techniques (linear and non-linear, fits to data with experimental errors, evaluating goodness of fit, etc) and error analysis, Handling of data and getting familiar with data analysis packages like IRAF, AIPS and CASA. This includes an introduction, beginners tutorials and exercises in these softwares as well as and X-ray data analysis.

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Overview of numerical computation – Simple problems: data sorting, root finding etc. - Numerical solutions of algebraic equations – Numerical integration, interpolation/extrapolation – Numerical differentiation – Ordinary differential equations – Partial differential equations – Statistics, Least-squares fitting – Data crunching, dealing large data set – Fourier transform – Advanced Applications in Astrophysics: N-Body Methods, Hydrodynamics – Monte Carlo Methods.

Overview of Solar system - Dynamics: Two-body problem, Three-Body Problem (Lagrangian points) - Resonances - Tidal forces - Solar energy balance and transport: Radiative Equilibrium - Planetary Atmospheres: Structure, Composition, Atmospheric Escape - Planetary surfaces: Surface morphology - Impact cratering - Minor Bodies: Meteories, Asteroids, Comets, Minor planets, Trans-Neptunian Objects, Centaurs - Planetary rings - Planet formation: Evolution of protoplanetary disks, Growth of solid bodies, Formation of Terrestrial and Giant planets - Planetary Migration: - Extrasolar Planets: Detecti

Concepts of Radiative Transfer – special relativity – Maxwell’s equations – Wave equation – retarded potentials – radiation field – Poynting vector – radiation from accelerated charge – bremsstrahlung – Thomson and Compton scattering – synchrotron radiation – thermal and non-thermal distribution of radiating particles – non-thermal synchrotron radiation – self-absorption – synchrotron and Compton cooling – Inverse Compton catastrophe and brightness temperature limit – propagation effects: dispersion, faraday rotation, depolarization – Atomic and molecular spectra – fine structure and hyperf

Telescopes and Detectors – optical, infrared, radio, x-rays, gamma-rays, neutrinos and cosmic rays; Gravitational radiation; Detection of dark matter and Dark Energy Astronomy from Space; Imaging – focal plane imagers, PSF and deconvolution, interferometry Photometry, Spectroscopy, Polarimetry, Astrometry; Solar telescopes; Surveys, Astronomical databases, Virtual Observatory.