The aim of this text is to introduce the beginner to the theory of
Riordan arrays. Starting in a simple and constructive manner, the
basic structure of these arrays is explained with clear examples,
before a more theoretical grounding is provided. Ordinary Riordan
arrays and exponential Riordan arrays are examined, with many
explicit examples, and their applications to combinatorics and
other areas are explored. The production matrix of a Riordan array
is shown to play a key role, along with various sequence
characterizations. Formal prerequisites are kept to a minimum, in
order to provide a gentle introduction to this exciting area, that
involves linear algebra, group theory and combinatorics. The reader
will be well positioned to further explore Riordan arrays and their
applications, and to undertake their own projects. They will join a
community of interested mathematicians that now spans all
continents, in a growing area of research and application.
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