INTRODUCTION The thirty-year-old research activity in the speech recognition area has pro- duced a well-consolidated technology based on Hidden Markov Models (HMMS) that is also firmly supported theoretically. The powerful capability of modeling complex (non-stationary) phenomena and the availability of efficient algorithms managing very large amounts of data extends the use of this tech- nology far beyond the specific task of speech recognition. This is not surprising considering that, initially, HMMS were thought to be applied to various predic- tion problems, like ecology and stock market behavior [Baum 67]. In recent years, sessions specifically devoted to HMM application on dif- ferent tasks are beginning to appear in most relevant congresses of the scientific community. Furthermore, HMM technology has been introduced into artificial intelligence tasks in the framework of Bayesian Networks. Relations between HMMS, Bayesian and Neural networks will be analyzed in Chapter 4. The HMM technology is now available for Automatic Speech Recognition (ASR) tasks owing to low-cost high-performance commercial products. Unfor- tunately, the essence of the technology cannot be understood using commercial products. In this sense, the Ford's assertion ("the technology is a real progress when it is available to anyone") is not fully pursued. In other words, technology de- tails are still confined to the few research laboratories that have invested large financial and research efforts in developing ASRS.