General Relativity, Cosmology and Astrophysics: Perspectives 100 years after Einstein's stay in Prag

Part I Gravity and Prague.- Kepler and Mach's Principle.- Einstein in Prague: Relativity Then and Now.- Part II Classical General Relativity.- Observers, observables and measurements in general relativity .- Some links between general relativity and other parts of physics.- The General Relativistic Two Body Problem and the Effective One Body Formalism.- Gravitational self-force: orbital mechanics beyond geodesic motion.- Hamiltonian formalism for spinning black holes in general relativity.- Stability of marginally outer trapped surfaces and geometric inequalities.- Stationary black-hole binaries: A non-existence proof.- Dynamic and Thermodynamic Stability of Black Holes and Black Branes.- Instability of anti-de Sitter spacetime.- Higher-dimensional black holes.- Black holes, hidden symmetry and complete integrability: Brief Review.- Part III Cosmology and Quantum Gravity.- Cosmological models and stability.- Inflation and Birth of Cosmological Perturbations.- Loop Quantum Gravity and The Planck Regime of Cosmology.- The inflationary origin of the seeds of cosmic structure: quantum theory and the need for novel physics.- Quantum Gravity: The view from particle physics.- Part IV Numerical Relativity and Relativistic Astrophysics.- Three little pieces for computer and relativity.- Instabilities of Relativistic Stars.- Gravity talks: observing the universe with gravitational waves.- LISA in 2012 and beyond - 20 years after the first proposal.- Einstein's gravity as seen by a cosmic lighthouse keeper.- The astrophysical signatures of black holes: the horizon, the ISCO, the ergosphere and the light circle.- Energy Extraction from Spinning Black Holes via Relativistic Jets.