This thesis deals with a robust finite-time adaptive law and its application to estimation and (distributed) control. Through the augmentation of a recently developed novel robust finite-time adaptive law to various schemes such as an adaptive observer (for the case of a single SISO system), an adaptive controller (for the case of a single MIMO system) and a distributed adaptive controller (for the case of multi SIMO and multi MIMO systems), robustness and finite-time convergence in the parameter estimation can be achieved. In contrast to conventional adaptive laws (e.g. gradient descent and least-square based method) which only guarantee exponential stability, robustness is 'achieved without compromising the need for finite-time convergence. Auxiliary filters are constructed exempting the algorithm from requiring state velocity (angular acceleration for the case of robotic manipulator control) in the adaptation algorithm. Capitalizing' on the use of a sliding mode-like switching term in the adaptation law coupled with the introduced auxiliary integrated regressors, the parameters are constructed within finite time. Finite-time convergence for consensus of a distributed cooperative (adaptive) control system is achieved by incorporating finite-time sliding surfaces in each connected agent in a network. Nonnegative matrix theory is extended to allow the Lyapunov analysis of the proposed finite-time distributed adaptive controller for multi-degree multi-manipulators. The algorithms are analysed using Lyapunov analysis to prove stability as well as robustness and finite-time convergence. Lyapunov function for the analysis with the case of bounded disturbance presence is also showcased. The algorithms have been successfully applied to an automotive problem to estimate road gradient and mass of vehicle, requiring engine torque and velocity only. The novel adaptive algorithm has been shown for the practical control of a robotic arm and for the cooperative control of two humanoid robotic manipulators for link and Cartesian coordinate control.