This book investigates the design of unknown input observers to asymptotically estimate unknown inputs of a broad class of dynamical systems, including systems with multiple time delays in both state and output vectors. The analysis is advanced by the introduction of generalized functionals, which provide a powerful framework for handling time-delay systems. This book presents recent advances alongside fundamental theory, offering researchers a valuable resource to understand the essential concepts and to explore state-of-the-art developments in unknown input and generalized functional estimation. It serves as a useful reference for researchers and postgraduate students working in control systems and can also support specialized senior undergraduate courses in control engineering and applied mathematics with a research focus.