Introduction to Neural Networks.- Preliminaries on Dynamical Systems and Stability Theory -- Survey of Dynamics of Cohen-Grossberg Type RNNs -- Delay-partitioning-method Based Stability Result for RNNs -- Stability result on the static and vector field recurrent neural networks -- Stability Criteria for RNNs Based on Secondary Delay Partitioning.- LMI-based Stability Criteria for Static Neural Networks -- Multiple Stability for Discontinuous RNNs -- LMI-based Passibity Criteria for RNNs with Delays -- Dissipativity and Invariant Sets for Neural Networks with Delay -- Synchronization Stability in Complex Neural Networks -- Stabilization of Stochastic RNNs with Stochastic Delays -- Adaptive Synchronization of Complex Neural Networks.