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The aircraft model used in this book is NASA`s F-18 HARV, a modified F-18 configuration that includes additional control surfaces (thrust vectoring and actuated nose strakes) in order to achieve better performance, maneuverability and increased flight envelope. A thoroughly analysis of the L1 adaptive control architecture is being performed. Two L1 adaptive controllers are designed, one for the SISO short period and the other for the MIMO lateral-directional dynamics. The L1 adaptive controllers are specially designed to compensate for matched and unmatched nonlinearities, unmodeled dynamics affecting the states and uncertainties affecting the control input. The inverse system required to compensate for the unmatched nonlinearities is obtained using a static output feedback approach that requires solving a rank constrain LMI problem. The L1 norm is computed by using Rutland and Lane`s algorithm. Finally, a path following algorithm that uses the ¿nonlinear guidance logic¿ is implemented and several simulations are performed. The intended audience includes researchers, engineers and Ph.D. students interested in dynamic systems modeling, adaptive control and numerical analysis.