Minimum Descriptive Length (MDL) principle, powerful method of inductive inference, argued that the best explanation, given a limited set of observed data, is one of the largest possible data compression? That the more we are able to compress the data, the more we learn about the regularity of the underlying data. Advances in Minimum Description Length is a resource book that will introduce the scientific community to the basics of MDL, the progress of recent theoretical, and practical applications. The book begins with an extensive tutorial on MDL, covering the basics of theoretical, practical implications as well as various interpretations, and its underlying philosophy.