Computer-based methods for the capture, construction, representation, fitting, interrogation and manipulation of complicated surfaces have led to a wide interest in, and need for, the mathematics of surfaces and related curves. Many applications require the use of surface descriptions, especially in such fields as computer aided design and manufacturing, computer graphics and computer vision. The description of surfaces is also of interest in geographic information systems, multimedia, and many other areas of science and medicine. This diversity and the wide range of applicability of the subject have already enabled the IMA to hold thirteen very successful international conferences in the Mathematics of Surfaces series. The 14th such conference has now been scheduled to be held at the University of Birmingham, UK, between 11-13 September 2013. Several international authorities are being invited to present papers. Papers will be reviewed by an international programme committee. Three types of papers are sought: Research papers presenting new developments in the capture, representation, manipulation, approximation, fitting, and design of surfaces, with an emphasis on computational methods and their underlying mathematical principles. Research papers covering novel practical applications of surface mathematics in areas such as CAD, computer vision, computer graphics, geographic information systems, and architecture, especially those which pose new problems for the research community. Survey papers describing the state of the art of an aspect of the mathematics of surfaces. This combination of topics will make the conference of interest to a wide audience of mathematicians, computer scientists, engineers and others. Contributions were sought covering parametric surfaces, implicit surfaces, mesh surfaces, and other representations. A key feature will be the interplay of ideas between the theoreticians in the subject and the users of the techniques. It is hoped that the conference will stimulate research ideas from users and developers of surface modelling systems by presentations of novel problems that may require new theoretical solutions.