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The main aim of the book is to present various types of neural networks and their stability properties illustrated by simulations. It is given several discrete models such as Hopfield-type delay impulsive neural networks, neural networks with non-instantaneous impulses and delays, and several continuous neural networks with switching topologies at impulsive times both deterministic as well as random. It is discussed different types of stability properties of the considered models. Also, it is studied the leader-following consensus problem for discrete multi-agent system with non-instantaneous impulses. Most of the theoretical results are illustrated by computer simulations. The study in the book is motivated by the potential applications of neural networks. It required the definitions and study of models which can more adequate describe the behavior in multi-agent systems. Much of the material presented in this book is based on the recent research of authors on the topic. The current book is intended for a wide audience, including Mathematicians, Applied Researchers, and Practitioners, whose interest extends beyond the boundaries of qualitative analysis of neural networks.