Warning-- slightly out of date! More up-to-date material, of a slightly different nature, is at kaldi.sourceforge.net.
Note: we originally planned to make videos of these lectures, but for technical reasons this did not happen.Lecture 1 (Overview of the course; getting started with Kaldi; feature generation)
Lecture 2 (HMMs; monophone training)
Lecture 3 (phonetic-context-dependent model training)
Lecture 4 (basic decoding)