These Proceedings contain a large part of the papers presented at the International Conference "Mathematics in Biology and Medicine" organized by the Dipartimento di Matematica and the Istituto di Igiene at the University of Bari, Italy, July 18-22, 1983. The main objective of the Conference was to bring together scientists in pure and applied mathematics and scientists in biology and medicine. The purpose was to exchange ideas and discuss the common problems encoun~red in the formulation, ana- lysis and numerical treatment of mathematical models in the biomedical sciences. Si- mulation methods and problems of validation of models vs. experimental data were al- so treated. SUrveys on recent mathematical results motivated by biological questioffi were given. Altogether,we think that a balance between mathematical and biomedical aspects was maintained. The Scientific Committee consisted of E. Biondi (Milano), P. Colli-Franzone (Udine), I. Galligani (Bologna), M. Iannelli (Trento), G. Koch (Roma), E. Marubini (Milano), C. Matessi (Pavia), M. Primicerio (Firenze), L.M. Ricciardi (Napoli), R. Rinaldi (Milano), A. Zampieri (Roma), and the European Liaison Committee consisted of R.M. Anderson (United Kingdom), N.T.J. Bailey (Switzerland), O. Diekmann (The Netherlands), K. Dietz (F. R. Germany), K.P. Hadeler (F* .*. R. Germany), J.P. Kernevez (France).