This chapter introduces Recursive Least Squares (RLS) as an advanced neural network training algorithm, presenting it as a specialized form of stochastic gradient descent that utilizes the inverse input autocorrelation matrix as an adaptive learning rate. The chapter provides a comprehensive mathematical derivation of the RLS algorithm, including the key equations for weight updates, covariance matrix recursion, and the role of the forgetting factor in emphasizing recent data. It demonstrates practical implementation through Python code for classification tasks using diabetes datasets, comparing RLS performance with traditional gradient descent methods and other machine learning algorithms. The theoretical foundation extends to convolutional neural networks, showing how RLS optimization can be applied to both convolutional and fully connected layers. The chapter concludes with empirical comparisons highlighting RLS’s faster convergence characteristics relative to conventional gradient descent approaches.