  In the 21st century, many of the crucial scientific and technical issues
facing humanity can be understood as problems associated with understanding,
modelling, and ultimately controlling complex systems: systems comprised of a
large number of non-trivially interacting components whose collective behaviour
can be difficult to predict. Information theory, a branch of mathematics
historically associated with questions about encoding and decoding messages,
has emerged as something of a lingua franca for those studying complex systems,
far exceeding its original narrow domain of communication systems engineering.
In the context of complexity science, information theory provides a set of
tools which allow researchers to uncover the statistical and effective
dependencies between interacting components; relationships between systems and
their environment; mereological whole-part relationships; and is sensitive to
non-linearities missed by commonly parametric statistical models.
  In this review, we aim to provide an accessible introduction to the core of
modern information theory, aimed specifically at aspiring (and established)
complex systems scientists. This includes standard measures, such as Shannon
entropy, relative entropy, and mutual information, before building to more
advanced topics, including: information dynamics, measures of statistical
complexity, information decomposition, and effective network inference. In
addition to detailing the formal definitions, in this review we make an effort
to discuss how information theory can be interpreted and develop the intuition
behind abstract concepts like "entropy," in the hope that this will enable
interested readers to understand what information is, and how it is used, at a
more fundamental level.
