1.2 deals with properties of functions of bounded 
The second chapter is devoted to the integral as defined by Jaroslav Kurzweil in [147]. We compiled some historical data on how the idea of the integral came about. Highlights of this chapter include the Saks–Henstock lemma, the Hake-type theorem, and the change of variables theorem. We end this chapter with a brief history of the Kapitza pendulum equation whose solution is highly oscillating and, therefore, suitable for being treated via Kurzweil–Henstock nonabsolute integration theory. An important reference to Chapter 2 is [209].
Before entering the theory of generalized ODEs, we take a trip through the theory of measure functional differential equations (we write measure FDEs for short). Then, the third chapter appears as an embracing collection of results on measure FDEs for Banach space-valued functions. In particular, we investigate equations of the form
where
In Chapter 4, we enter the theory of generalized ODE itself. We begin by recalling the concept of a nonautonomous generalized ODE of the form
where
This characteristic of generalized ODEs plays an important role in the entire manuscript, since it allows one to translate results from generalized ODEs to measure FDEs.
Chapter 5, based on [78], brings together the foundations of the theory of generalized ODEs. Section 5.1 concerns local existence and uniqueness of a solution of a nonautonomous generalized ODE with applications to measure FDEs and functional dynamic equations on time scales. Second 5.2 is devoted to results on prolongation of solutions of generalized ODEs, measure differential equations, and dynamic equations on time scales.
Chapter 6 deals with a very important class of differential equations, the class of linear generalized ODEs. The origins of linear generalized ODEs goes back to the papers [209–211]. Here, we recall the notion of fundamental operator associated with a linear generalized ODE for Banach space-valued functions and we travel on the same road as the authors of [45] to obtain a variation-of-constants formula for a linear perturbed generalized ODE. Concerning applications, we extend the class of equations to include linear measure FDEs.
After linear generalized ODEs are investigated, we move to results on continuous dependence of solutions on parameters. This is the core of Chapter 7 which is based on [4, 95, 96, 177]. Given a family of generalized ODEs, we present sufficient conditions so that the family of their corresponding solutions converge uniformly, on compact sets, to the solution of the limiting generalized ODE. We also prove that given a generalized ODE and its solution
As we mentioned before, many types of differential equations can be regarded as generalized ODEs. This fact allows us to derive stability results for these equations through the relations between the solutions of a certain equations and the solutions of a generalized ODEs. At the present time, the stability theory for generalized ODEs is undergoing a remarkable development. Recent results in this respect are contained in [3, 7, 80, 89, 90] and are gathered in Chapter 8. We also show the effectiveness of Lyapunov's Direct Method to obtain several stability results, in addition to proving converse Lyapunov theorems for some types of stability. The types of stability explore here are variational stability, Lyapunov stability, regular stability, and many relations permeating these concepts.
The existence of periodic solutions to any kind of equation is also of great interest, especially in applications. Chapter 9is devoted to this matter in the framework of generalized ODEs, whose results are also specified to measure differential equations and impulsive differential equations. Section 9.1 brings together a result which provides conditions for the solutions of a linear generalized ODE taking values in
