The main aim of the book is to present new constructive methods of delay differential equation (DDE) theory and to give readers practical tools for analysis, control design and simulating of linear systems with delays.  Referred to as “systems with delays” in this volume, this class of differential equations is also called delay differential equations (DDE), time-delay systems, hereditary systems, and functional differential equations.  Delay differential equations are widely used for describing and modeling various processes and systems in different applied problems At present there are effective control and numerical methods and corresponding software for analysis and simulating different classes of ordinary differential equations (ODE) and partial differential equations (PDE). There are many applications for these types of equations, because of this progress, but there are not as many methodologies in systems with delays that are easily applicable for the engineer or applied mathematician.  there are no methods of finding solutions in explicit forms, and there is an absence of generally available general-purpose software packages for simulating such systems.  Systems with Delays fills this void and provides easily applicable methods for engineers, mathematicians, and scientists to work with delay differential equations in their operations and research.