Preface. 50th Anniversary of the Founding of NATO. Dedication of the 7th Course to Ya.B. Zeldovich. 80th Anniversary of Professor I.M. Khalatnikov. I: The Early Universe. Phase Transitions in the Early Universe; M. Shaposhnikov. Elements of Baryogenesis; W. Buchmuller, S. Fredenhagen. Out of Equilibrium Fields in Selfconsistent Inflationary Dynamics. Density Fluctuations; D. Boyanovsky, H.J. de Vega. Minimal String Driven Cosmology and its Predictions; M.P. Infante, N. Sanchez. New Dual Relations Between Quantum Field Theory and String Regimes in Curved Backgrounds; M. Ramon Medrano, N. Sanchez. Detectability of Relic Squeezed Gravitational Waves by Laser Interferometers; L.P. Grishchuk. Gravitational Field and Its Energy-Momentum Tensor; L.P. Grishchuk, S.V. Babak. II: Cosmic Microwave Background Radiation. Observations and Theory of The Cosmic Microwave Background; A.N. Lasenby. The 1+3 Covariant Approach to CMB Anisotropies. Erice Lectures 1999; G.F.R. Ellis, P.K.S. Dunsby. Some Problems of the CMB Polarization; P. Naselsky, et al. The High Redshift Radio Universe; Yu.N. Parijskij. III: Large Scale Structure, Dark Matter. In Search of the Early Universe. I. The Oldest Stars; P.W. Hodge. In Search of the Early Universe. II. The Youngest Galaxies; P.W. Hodge. Clusters of Galaxies and the Large Scale Structure; G. Chincarini. Structure Formation of Galaxy Clusters and Beyond; L.-Z. Fang. Warm Dark Matter. Clues to Primordial Phase Density from the Structure of Galaxy Halos; C.J. Hogan. Dark Matter as Determined from Energetic Particles; P.L. Biermann. IV: Fractals and Scaling Laws in Astrophysics and Cosmology. Fractal Lacunarity andScenarios for the Near-Isotropic Distribution of Galaxies; B.B. Mandelbrot. Fractal Structures and the Large Scale Distribution of Galaxies; L. Pietronero, F.Sylos Labini. The Cosmological Many-Body Problem and Some of its Observational Implications; W.C. Saslaw. The Statistical Mechanics of the Self-Gravitating Gas: Equation of State and Fractal Dimension; H.J. de Vega, N. Sanchez. Renormalization Group Flow and Fragmentation in the Self-Gravitating Thermal Gas; B. Semelin, et al. V: High Energy and Neutrino Astrophysics. Bepposax: 3 Years of Operation. Highlights and Significant Results; L. Scarsi. The Extreme Energy Cosmic Rays and Cosmic Neutrinos as Probes for the Distant Universe. Astrophysics Involved and Experimental Approach; L. Scarsi. Origin and Physics of the Highest Energy Particles in the Universe; P.L. Biermann, et al. The Gamma-Ray Bursts and the SWIFT Mission; G. Chincarini, D. Lazzati. Neutrino Oscillations and Cosmology; A.D. Dolgov. High Energy Neutrino Astronomy: Towards Kilometer-Scale Detectors; F. Halzen. Accretion of Gas onto Black Holes; I.V. Artemova, et al. Mass Extinctions of Species Were Dinosaurs Killed by an Asteroid or Volcanoes? D.R.O. Morrison. Opening the Third Millennium. Photographs of the Institute. Author Index.