This book addresses physicists working in generalrelativity, astrophysics and cosmology. The contributionsare based on reports given at a summer school the goal ofwhich was to review modern research for students. The schoolwas centered on the study of gravitational fieldscorresponding to rotating objects of astrophysical interest,under different viewpoints: theoretical, numerical andobservational. Special emphasis is put on the analysis ofinterior and exterior fields of stationary axisymmetricsystems. Lectures and contributions, collected here in PartI, ranged from basic information useful to newcomers totechnical points pertaining to current research in thisarea. Part II contains lectures and contributions on otheraspects of gravitation theory. Equilibrium configurations of general relativistic rotating stars.- Axisymmetric stationary solutions of Einstein's equations.- The dyadic approach to solutions for rotating rigid bodies.- Stationary and axisymmetric perfect-fluid solutions to Einstein's equations.- Black-Holes in X-Ray Binaries.- General relativistic stationary axisymmetric rotating systems.- The superposition of two Kerr-Newman solutions.- Stationary black holes rotate differentially.- Differentially rotating perfect fluids.- Rotating barotropes.- Matching of stationary axisymmetric space-times.- Axial symmetry and conformal killings.- Numerical relativistic hydrodynamics.- Singularity-free spacetimes.- On radiative solutions in general relativity.- Application of Wahlquist-Estabrook method to relativity vacuum equations with one Killing vector.- On the regularity of spherically symmetric static spacetimes.- Shock capturing methods in 1D numerical relativity.- Invariance transformations of the class y? = F(x) y N of differential equations arising in general relativity.- Relativistic Kinetic Theory and cosmology.- Colliding gravitational waves with variable polarization.- The monopole - Quadrupole solution of Einstein's equations.- Effective action methods in cosmology: The back-reaction problem.- Quantization in a colliding plane wave spacetime.- Coleman's mechanism in Jordan-Brans-Dicke gravity.- No-boundary condition in multidimensional gravity.- Distance of matter inside an Einstein-Strauss vacuole.- Conformally stationary cosmological models.- L-Rigidity in Newtonian approximation.- Presymplectic manifolds and conservation laws.- On a project for a repetition of the Michelson - Morley experiment.- Nonlinear evolution of cosmological inhomogeneities.- The great attractor and the COBEquadrupole.
