Neural networks, or artificial neural networks (ANNs), are at the heart of machine learning, deep learning, and artificial intelligence. They are inspired by human brain dynamics and mimic the way that biological neurons communicate with one another. The first section introduces a brief history of ANNs and the basic theory is applied to simple logic gates. The second section covers feedforward and backpropagation, and the third section demonstrates how to train a simple neural network to value houses. The final section provides an introduction to neurodynamics using simple discrete models of neuromodules. A stability diagram is plotted which shows parameter regions where a system is in steady-state (period one), and unstable, bistable, and quasiperiodic (almost periodic) states.