The proposed doctoral qualification in Mathematics it aims to have a general nature, attending simultaneously and with quality the research training in all the specialisation fields of Mathematics, both in its basic and applied aspects. The general objective is to provide graduates with the level of specialised training required to develop a research career in Mathematics, both in the academic area and in research, development and innovation centres in the field of industry and new technologies. It is clearly evident the expansion of mathematical research in Spain in the last decades, which has allowed us to reach indicators of productivity and quality comparable to those of our neighbouring countries. However, the generational change of the research teams involved in this expansion may be threatened, among other reasons, by the uncertainty of a research career with little recognition, which causes a lower demand for specialised training by the new graduates in Mathematics. The renewal of research human resources in Mathematics is essential for the maintenance and progress of the competitiveness of Mathematics research in Spain and to increase the impact of this research on innovation and technological development. In this respect, we are convinced of the strategic interest of this qualification, which is proposed in order to consolidate not only research excellence in all areas of mathematics, but also its greater impact on society and technology transfer activities.