This volume of proceedings consists of the papers presented during the 9th International Workshop on Mathematical Methods in Scattering Theory and Biomedical Engineering, held in Patras, Greece, on 9-11 October 2009.The book contains papers on scattering theory and biomedical engineering — two rapidly evolving fields which have a considerable impact on today's research. All the papers are state-of-the-art, have been carefully reviewed before publication and the authors are well-known in the scientific community. In addition, some papers focus more on applied mathematics, which provides a solid ground for development and innovative research in scattering and biomedical engineering.