Preface. Thirty years of NATO in Erice. I: The Early Universe. The covariant and gauge invariant approach to perturbations in cosmology; G. F. R. Ellis. Lectures on inflationary cosmology; A. Linde. Back reactions of strings in self consistent string theory; H. J. de Vega, N. Sánchez. Topological defects in cosmology; E. P. S. Shellard. Cosmological inflation, microwave background anisotropies and large scale structure of the universe; D. S. Salopek. II: Cosmic Microwave Background. The big bang and the infrared sky as seen by COBE; J. C. Mather. Spectrum of the cosmic microwave background: Results and prospects; A. Kogut. Cosmic microwave background anisotropy spectrum from primordial density perturbations; G. F. Smoot. Cosmic microwave background anisotropy at large angular scales/ COBE DMR results; G. F. Smoot. COBE / DMR: Testing the initial conditions; A. Kogut. Detection of primary and secondary anisotropies in the CMB; A. Lasenby, S. Hancock. Small-scale fluctuations in the microwave sky: CBR fluctuations on sub-arcminute scales and sources of foreground noise; R. B. Partridge. Results and plans of CMB anisotropy observations (COBE, DMR, MAX and COBRAS); G. F. Smoot. III: Large Scale Structure. Dark matter and the value of Omega; C. S. Frenk. Dark matter and Sakharov oscillations; I. D. Novikov. Two lectures on the observational determination of the Hubble expansion rate; A. Sandage, G. A. Tammann. Photographs of the Institute. Author index. Subject index.