This document discusses Hidden Markov Models (HMM) and provides three examples to illustrate HMM concepts and the forward algorithm. It first defines Markov models and HMMs, noting that HMMs have hidden or unobserved states. It then gives examples of a coin toss process, a gambler tossing coins in a room, and using ice cream consumption and weather data to predict weather. It applies the forward algorithm to the ice cream/weather example to calculate the probability of a state path matching the observations over three days.