This is a collection of refereed papers presented at the 4th International Conference on Mathematical Population Dynamics. The selection of papers and their organization were made by the following persons: O. Arino, D. Axelrod, V. Capasso, W. Fitzgibbon, P. Jagers, M. Kimmel, D. Kirschner, C. Mode, B. Novak, R. Sachs. W. Stephan, A. Swierniak and H. Thieme. It features some of the new trends in cell and human population dynamics. The main link between the two traits is that human populations of concern here are essentially those subject to cell diseases, either the processes of anarchic proliferation or those by which some cell lines are killed by an infectious agent. The volume is divided into three main parts. Each part is subdivided into chapters, each chapter concentrating on a specific aspect. Each aspect is illustrated by one or several examples, developed in sections contributed by several authors. A detailed introduction for each part enables the reader to refer to chapters of interest. An index and a bibliography for each part is also included for easy reference.