The theme of the first Abel Symposium was operator algebras in a wide sense‎.‎ In the last 40 years operator algebras have developed from a rather special discipline within functional analysis to become a central field in mathematics often described as ‎"‎non‎-commutative geometry‎"‎‎.‎ It has branched out in several sub‎-disciplines and made contact with other subjects‎.‎ The contributions to this volume give a state‎-of‎-the‎-art account of some of these sub‎-disciplines and the variety of topics reflect to some extent how the subject has developed‎.‎ This is the first volume in a prestigious new book series linked to the Abel prize‎.‎