This volume is a thorough and comprehensive treatise on vector measures. The functions to be integrated can be either [0,infinity]- or real- or complex-valued and the vector measure can take its values in arbitrary locally convex Hausdorff spaces. Moreover, the domain of the vector measure does not have to be a sigma-algebra: it can also be a delta-ring. The book contains not only a large amount of new material but also corrects various errors in well-known results available in the literature. It will appeal to a wide audience of mathematical analysts.