Lectures given at the 1st Session of the Centro Internazionale Matematico Estivo (C.I.M.E.)

The summer school on Mathematics inspired by Biology was held at Martina Franca, Apulia, Italy in 1997. This volume presents five series of six lectures each. The common theme is the role of structure in shaping transient and ultimate dynamics. But the type of structure ranges from spatial (hadeler and maini in the deterministic setting, Durrett in the stochastic setting) to physiological (Diekmann) and order (Smith). Each contribution sketches the present state of affairs while, by including some wishful thinking, pointing at open problems that deserve attention.