Preface. Welcoming Address (P. Erdös). Random Graphs and Positional Games on the Complete Graph (J. Beck). A Note on Random Mappings: Convolutions and Partitions (S. Berg). On Matchings and Hamiltonian Cycles in Random Graphs (B. Bollobás and A.M. Frieze). Random Graphs of Small Order (B. Bollobás and A. Thomason). Vertex-Degrees in Strata of a Random Recursive Tree (M. Dondajewski, P. Kirschenhofer and J. Szymański). Reliability-Estimation in Stochastic Graphs with Time-Associated Arc-Set Reliability Performance Processes (W. Gaul). Electrical Networks with Random Resistances (G. Grimmett). A Random Bipartite Mapping (J. Jaworski). Probabilistic Inequalities from Extremal Graph Results (A Survey) (G.O.H. Katona). A New Version of the Solution of a Problem of Erdös and Rényi on Hamiltonian Cycles in Undirected Graphs (A.D. Korshunov). Locally Dependent Random Graphs and their Use in the Study of Epidemic Models (K. Kuulasmaa). A Random Sampling Procedure from a Finite Population and Some Applications (L. Mutafciev). Three Remarks on Dimensions of Graphs (J. Nešetřil and V. Rödl). Bipartite Complete Induced Subgraphs of a Random Graph (Z. Palka). Subgraphs of Random Graphs: A General Approach (A. Ruciński). Matchmaking Between Two Collections (L.H. Smit). Four Roads to the Ramsey Function (J. Spencer). Random Graph Problems in Polymer Chemistry (J.L. Spouge). Flows Through Complete Graphs (W.-C.S. Suen). On the Number of Trees Having k Edges in Common with a Caterpillar of Moderate Degrees (I. Tomescu). Random Graphs Almost Optimally Colorable in Polynomial Time (W.F. de la Vega). Subcube Coverings of Random Graphs in the n-Cube (K. Weber). Random Graphs and Polymerization Processes (P. Whittle). Critical Percolation Probabilities (J.C. Wierman).