Jump Time-Delay Systems (JTDS) represent a new class of piece-wise deterministic systems, in which the underlying dynamics is governed by delay-differential equations and it possesses multiple modes of operation depending on the value of an associated Markov random process. This book is about the time-domain modeling, stability, stabilization, control design and filtering for JTDS. It gives readers a thorough understanding of the basic mathematical analysis and fundamentals of JTDS. Additionally, it offers a straightforward treatment of the different topics and provides a broad coverage of the recent methodologies. The prime concern has been on the interplay between delay factors, jumping behavior and parametric uncertainties. The cases of single and interconnected JTDS are considered and numerous examples are worked out. The relationship to previous results on time-delay systems (TDS) and Markovian jump systems (MJS) are revealed.