"On Computable Numbers, with an Application to the Entscheidungsproblem", Alan Turing's paper of 1937, contained his thesis that every effective computation can be programmed on such an automation as that called Turing machine. Furthermore it proved the unsolvability of the halting problem and of the decision problem for first order logic, and it presented the invention of the universal Turing machine. It is that publication that will presumably be acknowledged as marking sub specie aeternitatis the beginning of the "computer age". This volume recognizes the still continuing influence of the Turing machine concept by collecting contributions from international specialists in logic, computability, mathematics, biology, physics, linguistics, and cognitive science, thus signalling the exceptionally wide scope of that concept.