We present an intelligent all-optical neural network using a single laser diode that is provided with controlled external feedback. The outputs of the laser neural network (LNN) are represented in the optical domain by the longitudinal cavity modes of the laser diode. The inputs to the LNN are applied by means of adjusting the external feedback of each longitudinal mode through an optical vector-matrix multiplier. Supervised training of some basic input-output mappings is demonstrated by means of a stochastic learning algorithm. The stability and reproducibility of the LNN setup is examined.