This book presents a collection of invited works that consider constructive methods for neural networks taken primarily from papers presented at a special th session held during the 18 International Conference on Artificial Neural Networks (ICANN 2008) in September 2008 in Prague Czech Republic. The book is devoted to constructive neural networks and other incremental learning algorithms that constitute an alternative to the standard method of finding a correct neural architecture by trial-and-error. These algorithms provide an incremental way of building neural networks with reduced topologies for classification problems. Furthermore these techniques produce not only the multilayer topologies but the value of the connecting synaptic weights that are determined automatically by the constructing algorithm avoiding the risk of becoming trapped in local minima as might occur when using gradient descent algorithms such as the popular back-propagation. In most cases the convergence of the constructing algorithms is guaranteed by the method used. Constructive methods for building neural networks can potentially create more compact and robust models which are easily implemented in hardware and used for embedded systems. Thus a growing amount of current research in neural networks is oriented towards this important topic. The purpose of this book is to gather together some of the leading investigators and research groups in this growing area and to provide an overview of the most recent advances in the techniques being developed for constructive neural networks and their applications.