This video introduces the probability transformation rule, for finding the probability density function of the mapping of another random variable. A derivation of the transformation rule is presented, by considering mutually exclusive small intervals, such that the rule is effectively an application of the axiomatic probability sum rule. An example with a single root is provided, leading to the log-normal distribution. The viewer is recommended to work through the example at the end of the inverse transformation of a random variable that is Cauchy distributed.