With the years the overlap among dierent research areas in Mathematics and Physics has been increasing steadily. This re ected on theWorkshop by introducing the word Integrability in its title, thus including in its programme a new research area deeply related to Mathematical Physics. Many deep and innovative results were reported during the Workshop; most of them are included in the present volume. A new positive trend in the activity of the Workshop was the increased number of young scientists from South Korea, Poland, Ireland and Bulgaria as well. This may give further new breed and stream to the forthcoming Workshops. With this volume we are paying deep respect to Professor Pierre Dolbeault from the Pierre et Marie Curie University, Paris. He participated in the 3rd Workshop at St. Konstantin and Elena, nearby Varna, in 1996 and was regarded as a teacher by many of the participants. We also congratulate Professor Julian Lawrynowicz from Lodz University, Poland for his 70-th birthday. Over the long years his regular and active participation has contributed a lot for their success.