This volume contains the full proceedings of the Fourth Advanced Study Institute organised by myself and my colleagues in . * the field of Communication Theory and Allied Subjects. In the first Institute we associated the subject of signal processing in communication with that in control engineering. Then we concentrated on noise and random phenomena by bringing in as well the subject of stochastic calculus. The third time our subject was multi-user communication and associated with it, the important problem of assessing algorithmic complexity. This time we are concerned with the vast increase of computational power that is now available in communication systems processors and controllers. This forces a mathematical, algorithmic and structural approach to the solution of computational requirements and design problems, in contrast to previous heuristic and intuitive methods. We are also concerned with the interactions and trade-offs between the structure, speed, and complexity of a process, and between software and hardware implementations. At the previous Advanced Study Institute in this series, on Multi-User Communications, there was a session on computational complexity, applied particularly to network routing problems. It was the aim of this Institute to expand this topic and to link it with information theory, random processes, pattern analysis, and implementation aspects of communication processors. The first part of these proceedings concentrates on pattern and structure in communications processing. In organising this session I was greatly helped and guided by Professor P. G. Farrell and Professor J. L. Massey.