Slowly, but surely, it is becoming a tradition that biannual international conf- enceson“VectorMeasuresandIntegration”aretakingplace.The?rstmeetingwas held in Valencia (Spain) in 2004 with the respectable total of 35 participants and the second meeting in Sevilla (Spain) in 2006with 50 participants.It became clear at the latter meeting that there was already a broader interest level in the area generally(asitshouldbe).Relatedareasfromoperatortheory,functionalanalysis, Banach (and Fr´ echet) spaces and lattices, non-commutative integration, function theory, classical and harmonic analysis, mathematical physics, and applied ma- ematics havetraditionallyused methods and techniquesfrom vector measuresand integration theory and, simultaneously, have themselves provided new problems, directions and impetus for the theory of vector measures and integration. So, for the third meeting, held in Eichst¨ att (Germany) in September 2008, a natural and deliberate step was taken to put a larger emphasis on applications andconnectionswith other areasofmathematics.Accordingly,the conferencetitle was modi?ed to “Vector Measures, Integration and Applications”, which is also re?ected in the title of this volume. Correspondingly, the attendance grew to 84 participants, which illustrates that the area is really thriving. Most importantly, there was also a healthy mixture of “oldies” and younger researchers in att- dance, coming from 21 countries. In addition, there was a pleasant and interesting combination of abstract theory, concrete applications and open problems. Needless to say, the fourth meeting is already ?xed; it will take place in late 2010 in Murcia (Spain). Thisvolumeconsistsofaselectionofrefereedpapersbasedontalkspresented at the conference. The included papers represent rather well most of the topics covered in the conference.