Error detecting codes are popular for error control in practical systems for two reasons. First, such codes can be used to provide any desired reliability of communication over any noisy channel. Second, implementation is usually much simpler than for a system using error correcting codes. To consider a particular code for use in such a system, it is important to be able to calculate/estimate the probability of undetected error. For the binary symmetric channel, the probability of undetected error can be expressed in terms of the weight distribution of the code. The first part of the book gives a description of known methods to calculate or estimate the probability of undetected error, for the binary symmetric channel in particular, but a number of other channel models are also considered. The second part of the book describes a number of protocols for feedback communication systems (ARQ systems), with methods for optimal choice of error detecting codes for the protocols.