Review of General Relativity: manifold, vectors, dual vectors, tensors, covariant differentiation, geodesic, Lie differentiation, Killing vector, curvature, geodesic deviation, Fermi normal coordinates, differential forms, tetrad formalism, Cartan’s structure equation, Einstein equation, Bianchi identities; The Expanding Universe: symmetric three-spaces, Robertson-Walker metric, geodesics, redshift, distances, perfect fluid, matter and radiation, dark energy, spacetime curvature, Friedmann equations, exact solutions, our universe; Hot Big Bang: some statistical mechanics, primordial plasma, entropy and expansion history, cosmic neutrino background, cosmic microwave background, Boltzmann equation, freeze-out, baryogenesis, big bang nucleosynthesis, recombination; Cosmic Inflation: the horizon problem, flatness problem, superhorizon correlators,  shrinking Hubble sphere, duration of inflation, scalar field dynamics, slow-roll inflation, creating the hot universe; Structure Formation: Newtonian perturbation theory, Jeans instability, linear growth function, transfer function, correlation functions, Gaussian random fields, Harrison-Zeldovich spectrum, spherical collapse, bound on Lambda; Relativistic Perturbation Theory: metric perturbations, matter perturbations, conservation equations, Einstein equations, superhorizon limit, adiabatic perturbations, curvature perturbation, primordial power spectrum, growth of matter perturbation, evolution of photon and baryons; Cosmic Microwave Background: angular power spectrum, gravitational redshift, light-of-sight solution, spatial to angular momentum projection, large and small scales, primordial sound waves, understanding power spectrum, LCDM cosmology, E and B modes; Quantum Initial Conditions: inflationary perturbations, equations of motion, quantum harmonic oscillators, inflationary power spectra, curvature perturbations, gravitational waves, slow-roll predictions, observational constraints.