Chapter 1. Introduction -- Chapter 2. Geometric Tools for Time Delay Systems -- Chapter 3. The Geometric Framework - Results on Integrability -- Chapter 4. Accessibility of Nonlinear Time-Delay Systems -- Chapter 5. On the Geometric Interpretation of the Polynomial Lie Bracket -- Chapter 6. Observability -- Chapter 7. Characterization of the Chain Form with Delays -- Chapter 8. Applications of Integrability -- Chapter 9. Control of Single-Input Time Delay Systems.

This brief focuses on the structural properties of nonlinear time-delay systems. It provides a link between coverage of fundamental theoretical properties and advanced control algorithms, as well as suggesting a path for the generalization of the differential geometric approach to time-delay systems . The brief begins with an introduction to a class of single-input nonlinear time-delay systems. It then focuses on geometric methods treating them and offers a geometric framework for integrability. The book has chapters dedicated to the accessibility and observability of nonlinear time-delay systems, allowing readers to understand the systems in a well-ordered, structured way. Finally, the brief concludes with applications of integrability and the control of single-input time-delay systems. This brief employs exercises and examples to familiarize readers with the time-delay context. It is of interest to researchers, engineers and postgraduate students who work in the area of nonlinear control systems.