This is an announcement for the paper "Volume inequalities and additive maps of convex bodies" by Franz E. Schuster. Abstract: Analogues of the classical inequalities from the Brunn-Minkowski theory for rotation intertwining additive maps of convex bodies are developed. Analogues are also proved of inequalities from the dual Brunn-Minkowski theory for intertwining additive maps of star bodies. These inequalities provide generalizations of results for projection and intersection bodies. As a corollary, a new Brunn-Minkowski inequality is obtained for the volume of polar projection bodies. Archive classification: math.MG math.DG math.FA Mathematics Subject Classification: 52A40, 52A39 Citation: Mathematika 53 (2006), 211–234 Submitted from: franz.schuster@tuwien.ac.at The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1207.7290 or http://arXiv.org/abs/1207.7290