Artificial neural networks (ANN) are widely used in diverse fields of science and industry. Though there have been numerous techniques used for their implementations, the choice of a specific implementation is subjected to different factors including cost, accuracy, processing speed and overall performance. Featured with synaptic plasticity, the process of training is concerned with adjusting the individual weights between each of the individual ANN neurons until we can achieve close to the desired output. This book introduces the common trajectory-driven and evolutionary-based ANN training algorithms.