This is an introduction to the by now fifteen years old research field of canonical quantum general relativity, sometimes called "loop quantum gravity". The term "modern" in the title refers to the fa . . . . .

Contents: Introduction; Special Relativity and Flat Spacetime; Manifolds; Curvature; Gravitation; More Geometry; Weak Fields and Gravitational Radiation; The Schwarzschild Solution and Black Holes; Co . . . . .

In the framework of the special theory of relativity, the relativistic theory of gravitation (RTG) is constructed. The energy-momentum tensor density of all the matter fields (including gravitational . . . . .

These lecture notes provide some introduction to the 3 plus 1 formalism of general relativity, which is the foundation of most modern numerical relativity. The text is rather self-contained, with deta . . . . .

These are lecture notes of an introductionary course on General Relativity done in the years 1998-2003 in the framework of the ICTP Diploma Course.

Contenu: observateurs, espaces-temps et lois de la dynamique; Theorie de Newton de la gravitation; elements de calcul tensoriel en espace affine; elements de geometrie differentielle d'une variete; th . . . . .

Contents: Introduction; Curves; Gauss Curvature; Surfaces in E3; First Fundamental Form; Second Fundamental Form; The Gauss Curvature in Detail; Geodesics; The Curvature Tensor and the Theorema Egregi . . . . .

Chern-Simons modified gravity is an effective extension of general relativity that captures leading-order, gravitational parity violation. Such an effective theory is motivated by anomaly cancelation . . . . .

Topics include: Asymptotic structure of spacetime, conformal diagrams, null surfaces, Raychaudhury equation, black holes, the holographic principle, singularity theorems, Einstein-Hilbert action, ener . . . . .

Contents: Summary of the theory of Special Relativity; The Eotvos experiment and the equivalence principle; The constantly accelerated elevator , Rindler space; Curved Coordinates; The affine connecti . . . . .

After explaining the physical motivations we first introduce curved coordinates, then add to this the notion of an affine connection field and only as a later step add to that the metric field. One th . . . . .

This is an introduction to the by now fifteen years old research field of canonical quantum general relativity, sometimes called \\\"loop quantum gravity\\\". (301 pages)

Contents: 1) Introduction and a few excursions 2) The Schwarzschild solution 3) The Reissner- Nordstrom solution 4) The Kerr metric 5) Black hole uniqueness and multi-black hole solutions 6) Stati . . . . .