We present a system for robust robot skill acquisition from kinesthetic demonstrations. This system allows a robot to learn a simple goal-directed gesture, and correctly reproduce it despite changes in the initial conditions, and perturbations in the environment. It combines a dynamical system control approach with tools of statistical learning theory and provides a solution to the inverse kinematics problem, when dealing with a redundant manipulator. The system is validated on two experiments involving a humanoid robot: putting an object into a box, and reaching for and grasping an object.