This talk will be an introduction to the basic ideas of coalgebra and
coinduction and their impact on computer science over the last decade. I will
talk about notions of bisimilarity, final coalgebra constructions, greatest and least
fixpoints, initial algebras and final coalgebras, coterms and applications
to logic, and coinduction as a method of proof. I will illustrate the main ideas
through examples involving infinite streams, automata, power series,
and coinductive datatypes in programming languages.