This e-book is devoted to the research of Professor Yves Cherruault and his colleagues at MEDIMAT, Université Pierre et Marie Curie – Paris VI, France. Professor Cherruault and his colleagues are already recognised worldwide for their contribution to the fields of mathematical modeling and mathematical methods pertaining to the life sciences. The first section of this e-book deals with methodology, and newly devised versions of the world-acclaimed Adomian and Alienor methods. The second section looks at the applications of these methods to identification and optimal control. The third section lists brief research summaries of current work in progress.