This volume provides an up-to-date view of several topics in theoretical computer science and suggests directions for future research. It constitutes a valuable working tool for mathematicians, electrical engineers and computer scientists and will be of interest to researchers and graduate students in combinatorics, cryptography, information compression and transmission, or mathematics applied to engineering. Among the contributions to this volume, all by world-renowned scientists, are: Ramsey theory applied to showing the existence of arithmetic subsequences with applications to molecular biology; methods for finding the smallest possible Markov Chain that could produce a given sequence of numbers; construction of pseudo-random arrays; the relationship between stochastic complexity and data compression; string matching algorithms; parallel algorithms for string matching in various contexts; string and picture compression; dynamic data compression; coding sequences with constraints; universal sequences for graphs; coding theory; combinatorial issues, including techniques for designing error-correcting codes; and applications of information theory to external set theory. In addition, there are various contributions in related subjects such as distributed computing, approximation algorithms, and cryptography.