This book contains all papers presented at the 1998 International Conference on Sequences and Their Applications (SETA8) that passed a strict refereeing process. It consists of several survey papers by leading experts and a number of research papers on sequences and their applications. This book gives the state of the art of both the theory of sequences and their applications in cryptography, coding theory, communications systems, numerical computation, and computer simulation. In this book the reader will find connections between sequences and a number of mathematical fields such as automata, algebraic function fields, combinatorics, finite fields, Galois rings, geometry, graph theory, and number theory. Of course the reader will find vast applications of sequences. This book should be of interest to mathematicians, computer scientists, cryptographers, and communications engineers. '