Method of Guiding Functions in Problems of Nonlinear Analysis 1 Background 2 MGF in Finite Dimensional Spaces 3 Guiding Functions in Hilbert Spaces. 4 Second Order Differential Inclusions. 5 Nonlinear Fredholm Inclusions. This book offers a self contained introduction to the theory of guiding functions methods which can be used to study the existence of periodic solutions and their bifurcations in ordinary differential equations differential inclusions and in control theory. It starts with the basic concepts of nonlinear and multivalued analysis describes the classical aspects of the method of guiding functions and then presents recent findings only available in the research literature. It describes essential applications in control theory the theory of bifurcations and physics making it a valuable resource not only for “pure” mathematicians but also for students and researchers working in applied mathematics the engineering sciences and physics.