The Scottish Doctoral Training Centre in Condensed Matter Physics, known as the CM-DTC, is an EPSRC-funded Centre for Doctoral Training (CDT) addressing the broad field of Condensed Matter Physics (CMP). CMP is a core discipline that underpins many other areas of science, and is one of the Priority Areas for this CDT call. Renewal funding for the CM-DTC will allow five more annual cohorts of PhD students to be recruited, trained and released onto the market. They will be highly educated professionals with a knowledge of the field, in depth and in breadth, that will equip them for future leadership in a variety of academic and industrial careers. Condensed Matter Physics research impacts on many other fields of science including engineering, biophysics, photonics, chemistry, and materials science. It is a significant engine for innovation and drives new technologies. Recent examples include the use of liquid crystals for displays including flat-screen and 3D television, and the use of solid-state or polymeric LEDs for power-saving high-illumination lighting systems. Future examples may involve harnessing the potential of graphene (the world's thinnest and strongest sheet-like material), or the creation of exotic low-temperature materials whose properties may enable the design of radically new types of (quantum) computer with which to solve some of the hardest problems of mathematics. The UK's continued ability to deliver transformative technologies of this character requires highly trained CMP researchers such as those the Centre will produce. The proposed training approach is built on a strong framework of taught lecture courses, with core components and a wide choice of electives. This spans the first two years so that PhD research begins alongside the coursework from the outset. It is complemented by hands-on training in areas such as computer-intensive physics and instrument building (including workshop skills and 3D printing). Some lecture courses are delivered in residential schools but most are videoconferenced live, using the well-established infrastructure of SUPA (the Scottish Universities Physics Alliance). Students meet face to face frequently, often for more than one day, at cohort-building events that emphasise teamwork in science, outreach, transferable skills and careers training. National demand for our graduates is demonstrated by the large number of companies and organisations who have chosen to be formally affiliated with our CDT as Industrial Associates. The range of sectors spanned by these Associates is notable. Some, such as e2v and Oxford Instruments, are scientific consultancies and manufacturers of scientific equipment, whom one would expect to be among our core stakeholders. Less obviously, the list also represents scientific publishers, software houses, companies small and large from the energy sector, large multinationals such as Solvay-Rhodia and Siemens, and finance and patent law firms. This demonstrates a key attraction of our graduates: their high levels of core skills, and a hands-on approach to problem solving. These impart a discipline-hopping ability which more focussed training for specific sectors can complement, but not replace. This breadth is prized by employers in a fast-changing environment where years of vocational training can sometimes be undermined very rapidly by unexpected innovation in an apparently unrelated sector. As the UK builds its technological future by funding new CDTs across a range of priority areas, it is vital to include some that focus on core discipline skills, specifically Condensed Matter Physics, rather than the interdisciplinary or semi-vocational training that features in many other CDTs. As well as complementing those important activities today, our highly trained PhD graduates will be equipped to lay the foundations for the research fields (and perhaps some of the industrial sectors) of tomorrow.