We've got several research oriented tutorials available currently, with more to come:
The spectrogram reading tutorial is a great place to gain an understanding of what a speech signal looks like and what sort of spectral features are used in speech analysis. You can even learn how to how you can "read" a speech signal without even hearing it!
The robust natural-language parsing tutorial will introduce robust parsing and the CSLU robust parser PROFER (Predictive, RObust, Finite-state parsER) through a series of exercises.
Neural networks and Hidden Markov Model (HMM) systems are the subject of several tutorials. There is a section describing how neural networks are used for speech recognition, and one on building a hybrid neural-network based speech recognizer.