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Humans are very efficient in learning new skills through imitation and social interaction with other individuals. Recent experimental findings on the functioning of the mirror neuron system in humans and animals and on the coding of intentions, have led to the development of more realistic and powerful models of action understanding and imitation. This paper describes the implementation on a humanoid robot of a spiking neuron model of the mirror system. The proposed architecture is validated in an imitation task where the robot has to observe and understand manipulative action sequences executed by a human demonstrator and reproduce them on demand utilizing its own motor repertoire. To instruct the robot what to observe and to learn, and when to imitate, the demonstrator utilizes a simple form of sign language. Two basic principles underlie the functioning of the system: 1) imitation is primarily directed toward reproducing the goals of observed actions rather than the exact hand trajectories; and 2) the capacity to understand the motor intentions of another individual is based on the resonance of the same neural populations that are active during action execution. Experimental findings show that the use of even a very simple form of gesture-based communication allows to develop robotic architectures that are efficient, simple and user friendly.