Combinatorics is one of the fastest growing fields of mathematics. One reason for this is because many practical problems can be modeled and then efficiently solved using combinatorial theory. This real world motivation for studying algorithmic combinatorics has led not only to the development of many software packages but also to some beautiful mathematics which has no direct application to applied problems. This book highlights a few of the exciting recent developments in algorithmic combinatorics, including the search for patterns in DNA and protein sequences, the theory of semi-definite programming and its role in combinatorial optimization, and the algorithmic aspects of tree decompositions and it's applications to the theory of databases, code optimization, and bioinformatics. Claudia Linhares-Sales is Assistant Professor of Computer Science at the Federal University of Cear, Brazil. Bruce Reed is Canada Research Chair in Graph Theory at the School of Computer Science of McGill Univeristy.