In 1990 a workshop on the Mathematical Concepts (or Principles) of Dependable Systems was held at the Mathematisches Forschungsinstitut Oberwolfach in Germany. The purpose of the workshop was to examine mathematical techniques developed to make it possible to prove the proper functioning of complex systems--where the system could be either hardware, software, information protocols, etc., or combinations of these components. Principal researchers in each of these areas were invited to take part in the workshop, and did--but as is so often the case at scientific meetings, one area emerged as a clear center of gravity for the workshop. This was the topic of applying formal methods to the proof of soundness or correctness of information or cryptographic protocols. The organizers of the workshop felt that the results reported in this area were so important to the cryptology community they deserved publication as a whole, as opposed to publication as separate and isolated papers: hence this special section. This paper, which is essentially an introduction for the invited paper that follows, describes the background for the workshop and the challenge problem(s) that provided a unifying theme for the three systems of formal analysis treated in it.