This report explains the theory of Hidden Markov Models (HMMs). The emphasis is on the theory aspects in conjunction with the implementation issues that are encountered in a floating point processor. The main theory and implementation issues are based on the use of a Gaussian Mixture Model (GMM) as the state density in the HMM, and a Continuous Density Hidden Markov Model (CDHMM) is assumed. Suggestions and advice related to the implementation are given for a typical pattern recognition task.