1. Introduction to Neural Networks and Mathematica. 1.1. The Neural-Network Paradigm. 1.2. Neural-Network Fundamentals -- 2. Training by Error Minimization. 2.1. Adaline and the Adaptive Linear Combiner. 2.2. The LMS Learning Rule. 2.3. Error Minimization in Multilayer Networks -- 3. Backpropagation and Its Variants. 3.1. The Generalized Delta Rule. 3.2. BPN Examples. 3.3. BPN Variations. 3.4. The Functional Link Network -- 4. Probability and Neural Networks. 4.1. The Discrete Hopfield Network. 4.2. Stochastic Methods for Neural Networks. 4.3. Bayesian Pattern Classification. 4.4. The Probabilistic Neural Network -- 5. Optimization and Constraint Satisfaction. 5.1. The Traveling Salesperson Problem (TSP). 5.2. Neural Networks and the TSP -- 6. Feedback and Recurrent Networks. 6.1. The BAM. 6.2. Recognition of Time Sequences -- 7. Adaptive Resonance Theory. 7.1. ART1. 7.2. ART2 -- 8. Genetic Algorithms. 8.1. GA Basics. 8.2. A Basic Genetic Algorithm (BGA). 8.3. A GA for Training Neural Networks -- Appendix A Code Listings.