Basicdefinitions Concerning the Multi-Layer Feed-Forward Neural Networks Are Given.The Back-Propagation Training AlgoRithm Is Explained. Partial Derivatives Ofthe Objective Function With Respect to the Weight and Threshold Coefficientsare DeRived. These Derivatives Are Valuable For an Adaptation Process of Theconsidered Neural Network. Training and Generalisation of Multi-Layerfeed-Forward Neural Networks Are Discussed. Improvements of the Standardback-Propagation Algorithm Are ReViewed. Example of the Use of Multi-Layerfeed-Forward Neural Networks For Prediction of Carbon-13 Nmr Chemical Shifts Ofalkanes Is Given. Further Applications of Neural Networks In Chemistry Arereviewed. Advantages and Disadvantages of MultiLayer Feed-Forward Neuralnetworks Are Discussed.