The adaptive linear combiner is the fundamental building block of all neural networks, and of all adaptive filters in signal processing and control applications. The coefficients or weights of the linear combiner are adjusted automatically by an adaptive algorithm. In most cases, this algorithm is known as LMS (Least Mean Squares). The linear combiner is trainable. The training involves input vectors or patterns presented to the combiner, along with corresponding desired responses. The training objective is to adjust the combiner’s parameters so as to cause the pattern responses to match to the greatest degree as possible the desired responses (in the least mean squares sense). The mean-square-error is a quadratic function of the parameters. A stochastic gradient is used with the method of steepest descent to seek the optimal solution at the bottom of the quadratic “bowl.” The resulting LMS algorithm is perhaps the simplest of all adaptive algorithms. It is used widely in engineering applications and appears to be a natural algorithm, part of nature’s process for learning and adaptation. This chapter is based verbatum on Chapter 3 of Cybernetics 2.0 [8].