The 18 research articles of this volume discuss the major themes that have emerged from mathematical and statistical research in the epidemiology of HIV. The opening paper reviews important recent contributions. Five sections follow: Statistical Methodology and Forecasting, Infectivity and the HIV, Heterogeneity and HIV Transmission Dynamics, Social Dynamics and AIDS, and The Immune System and The HIV. In each, leading experts in AIDS epidemiology present the recent results. Some address the role of variable infectivity, heterogeneous mixing, and long periods of infectiousness in the dynamics of HIV; others concentrate on parameter estimation and short-term forecasting. The last section looks at the interaction between the HIV and the immune system.