Natural duality theory is one of the major growth areas within
general algebra. This text provides a short path to the forefront
of research in duality theory. It presents a coherent approach to
new results in the area, as well as exposing open problems.
Unary algebras play a special role throughout the text.
Individual unary algebras are relatively simple and easy to work
with. But as a class they have a rich and complex entanglement with
dualisability. This combination of local simplicity and global
complexity ensures that, for the study of natural duality theory,
unary algebras are an excellent source of examples and
counterexamples.
A number of results appear here for the first time. In
particular, the text ends with an appendix that provides a new and
definitive approach to the concept of the rank of a finite algebra
and its relationship with strong dualisability.
General
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