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We present a method for autonomous learning of dextrous manipulation skills with multifingered robot hands. We use heuristics derived from observations made on human hands to reduce the degrees of freedom of the task and make learning tractable. Our approach consists of learning and storing a few basic manipulation primitives for a few prototypical objects and then using an associative memory to obtain the required parameters for new objects and/or manipulations. The parameter space of the robot is searched using a modified version of the evolution strategy, which is robust to the noise normally present in real-world complex robotic tasks. Given the difficulty of modeling and simulating accurately the interactions of multiple fingers and an object, and to ensure that the learned skills are applicable in the real world, our system does not rely on simulation; all the experimentation is performed by a physical robot, in this case the 16-degree-of-freedom Utah/MIT hand. Experimental results show that accurate dextrous manipulation skills can be learned by the robot in a short period of time. We also show the application of the learned primitives to perform an assembly task and how the primitives generalize to objects that are different from those used during the learning phase.