The main aim of this book is the detail analysis of training algorithms of ANN such as back propagation and we discuss how to increase the speed of these algorithms. Back propagation can train multilayer feed forward networks with differentiable transfer functions to perform function approximation, pattern association, and pattern classification. The term back propagation refers to the process by which derivatives of the neural network error with respect to the neural network weights and biases can be computed. This process can be used with a number of different optimization strategies. In another word we known that the standard back propagation is based on the gradient descent, but one of the draw backs of using gradient descent for minimization of the performance function is that the algorithm may converge to a local minimum in the error surface.The architecture of a multilayer ANN depend on the problem to be solved.The number of inputs to the ANN is constrained by the problem, and the number of neurons in the output layer is constrained by the number of outputs required by the problem. A three layer sigmoid/linear network can represent any functional model.