This paper presents a systematic design method for adaptive controllers for feedback linearizable nonlinear systems. The approach is based on coordinate-free geometric conditions that characterize the class of systems, which do not restrict the location of unknown parameters or the growth of nonlinearities. Instead, they require that the system be transformable into the so-called pure-feedback form. When this form is "strict," the proposed scheme guarantees global regulation and tracking properties. The design procedure interlaces coordinate transformations with the construction of parameter update laws. The method uses simple analytical tools and provides a straightforward Lyapunov argument for stability. The paper also extends the design to multi-input systems and presents a global tracking result for input-output linearizable systems with exponentially stable zero dynamics. The approach is shown to be globally stable and effective for a broad class of nonlinear systems.This paper presents a systematic design method for adaptive controllers for feedback linearizable nonlinear systems. The approach is based on coordinate-free geometric conditions that characterize the class of systems, which do not restrict the location of unknown parameters or the growth of nonlinearities. Instead, they require that the system be transformable into the so-called pure-feedback form. When this form is "strict," the proposed scheme guarantees global regulation and tracking properties. The design procedure interlaces coordinate transformations with the construction of parameter update laws. The method uses simple analytical tools and provides a straightforward Lyapunov argument for stability. The paper also extends the design to multi-input systems and presents a global tracking result for input-output linearizable systems with exponentially stable zero dynamics. The approach is shown to be globally stable and effective for a broad class of nonlinear systems.