  This is an up-to-date introduction to and overview of the Minimum Description
Length (MDL) Principle, a theory of inductive inference that can be applied to
general problems in statistics, machine learning and pattern recognition. While
MDL was originally based on data compression ideas, this introduction can be
read without any knowledge thereof. It takes into account all major
developments since 2007, the last time an extensive overview was written. These
include new methods for model selection and averaging and hypothesis testing,
as well as the first completely general definition of {\em MDL estimators}.
Incorporating these developments, MDL can be seen as a powerful extension of
both penalized likelihood and Bayesian approaches, in which penalization
functions and prior distributions are replaced by more general luckiness
functions, average-case methodology is replaced by a more robust worst-case
approach, and in which methods classically viewed as highly distinct, such as
AIC vs BIC and cross-validation vs Bayes can, to a large extent, be viewed from
a unified perspective.
