The study of fixed wing aeronautical engineering has matured to the point where years of research result in small performance improvements.  In the past decade, micro air vehicles, or MAVs, have gained attention of the aerospace and robotics communities.  Many researchers have begun investigating aircraft schemes such as ones which use rotary or flapping wings for propulsion.  While the engineering of rotary wing aircraft has seen significant advancement, the complex physics behind flapping wing aircraft remains to be fully understood.  Some studies suggest flapping wing aircraft can be more efficient when the aircraft operates in low Reynolds regimes or requires hovering.  Because of this inherent complexity, the derivation of flapping wing control methodologies remains an area with many open research problems.  This thesis investigates flapping wing vehicles whose design is inspired by avian flight.  The flapping wing system is examined in the cases where the core body is fixed or free in the ground frame.  When the core body is fixed, the Denavit Hartenberg representation is used for the kinematic variables.  An alternative approach is introduced for a free base body case.  The equations of motion are developed using Lagranges equations and a process is developed to derive the aerodynamic contributions using a virtual work principle.  The aerodynamics are modeled using a quasi-steady state formulation where the lift and drag coefficients are treated as unknowns.  A collection of nonlinear controllers are studied, specifically an ideal dynamic inversion controller and two switching dynamic inversion controllers.  A dynamic inversion controller is modified with an adaptive term that learns the aerodynamic effects on the equation of motion.  The dissipative controller with adaptation is developed to improve performance.  A Lyapunov analysis of the two adaptive controllers guarantees boundedness for all error terms.  Asymptotic stability is guaranteed for the derivative error in the dynamic inversion controller and for both the position and derivative error in the dissipative controller.  The controllers are simulated using two dynamic models based on flapping wing prototypes designed at Virginia Tech.  The numerical experiments validate the Lyapunov analysis and illustrate that unknown parameters can be learned if persistently excited. / Master of Science