In this thesis we present a novel solution to the kite trajectory tracking problem using an explicit control law. Compared to alternative approaches, such as model predictive control, our approach has three major advantages: a stability proof, ease of implementation, and minimal modeling requirements. The latter is especially important for control of flexible kites, which are hard to model accurately in a point-mass or rigid-body framework. Kites commonly have a single control input available for steering. We show how the differential-geometric notion of turning angle can be used as a one-dimensional representation of the kite trajectory, and how this leads to a single-input single-output tracking problem. In order to facilitate model inversion we linearize the turning angle dynamics in the steering control input, and apply energy methods to derive a stabilizing feedback law. We show how the zero-term of the linearization can be measured directly using on-board sensors, and how in this way the control law comes to depend on the control derivatives of the aerodynamic kite model only. The controller adapts the estimates of these control derivatives based on tracking performance. Repeated simulations with a point-mass model show our control approach to be robust against turbulence, and simulations with a multi-body model of a flexible kite validate our modeling assumptions.