First we shall see what a coalgebra is, and a number of examples involving input, output, nondeterminism, divergence and (discrete) probability. In particular, we look at final coalgebras, which are used to represent data types such as lazy lists and lazy trees. We look at various kinds of simulation and bisimulation, and see how they can be brought together using the notion of a relator. Finally we see that simulation and bisimulation can be characterized using a final coalgebra, and conversely that we can construct a final coalgebra by taking an extensional quotient.
Here is a draft of the course notes.