In my thesis I recollect the proof of Rabin's Theorem on the decidability of Monadic second-order logic of infinite binary tree structures improved in various aspects. The underlying constructions are adapted from coalgebraic automata theory recently introduced by my supervisors Yde Venema and Clemens Kupke. Apart from the closure under complementation, the proof indeed generalises to arbitrary coalgebra automata. The defense was on 29 August 2007. If you have missed it, a revised version and the slides are available.