This chapter consider a simple example to motivate the hidden Markov model (HMM) formulation. HMMs are based on discrete probability. While the formulation of HMMs might initially seem somewhat contrived, there exist a virtually unlimited number of problems where the technique can be applied. Dynamic programming (DP) can be used to efficiently solve this problem. On the other hand, we might reasonably define "most likely" as the state sequence that maximizes the expected number of correct states. An HMM can be used to find the most likely hidden state sequence. The chapter summarises the notation used in an HMM. It considers critical computational issues that must be addressed when writing any HMM computer program. HMM are powerful, efficient, and extremely useful in practice. Virtually no assumptions need to be made, yet the HMM process can extract significant statistical information from data.