This book is a trail-blazer in robust formulations, investigations of computational feasibility and electronic implementations of mathematical results. It developed and used the core concept and computable expressions for determining matrices to establish necessary and sufficient conditions for Euclidean controllability of certain classes of functional differential systems. To actualize the applications of variation of constants formulas for initial and terminal function problems, as well as the characterization of controllability in terms of indices of control systems, this book pioneered the formulation and validation of the expressions and structures of solution and control index matrices for some classes of hereditary systems. To eliminate all computational and implementation constraints and achieve large¿scale industrial applicability of the results, the book developed and provided software codes with a user guide for the implementation of results on the C++ platform. This has placed the generally neglected implementation aspect of mathematical results on the front burner, thus providing implementation paradigm shift.