  This paper is a first step to chase the ambitious objective of developing a
mathmatical theory of living systems. The contents refer modeling large systems
of interacting living entities with the aim of describing their collective
behaviors by differential models. The contents is in three parts. Firstly, we
derive the mathematical method; subsequently, we show how the method can be
applied in a number of case studies related to well defined living systems and
finally, we look ahead to research perspectives focusing both on mathematical
methods and further applications.
