In this chapter, a backpropagation algorithm is introduced for the learning of a neural network. The major contributions of this chapter are as follows: (1) A theorem to assure the uniform stability of the general discrete-time systems is proposed, (2) it is proven that the backpropagation algorithm with a new time varying rate is uniformly stable for online identification, and the identification error converges to a small zone bounded by an uncertainty, (3) it is proven that the weights’ error is bounded by the initial weights’ error, i.e., the overfitting is not presented in the proposed algorithm, (4) the backpropagation is applied to predict the distribution of loads that a transelevator receives from a trailer and places in the deposits each hour in a warehouse, and the deposits in the warehouse can be reserved in advance using the prediction results, (5) the backpropagation algorithm is compared with the recursive least square algorithm and the Sugeno fuzzy inference system in the problem of the prediction of the distribution of loads in a warehouse, giving that the first and the second are stable and the third is unstable, and (6) the backpropagation algorithm is compared with the recursive least square algorithm and the Kalman filter algorithm in an academic example.