Risk is the potential of experiencing a loss when a system does not operate as expected due to uncertainties. Its assessment requires the quantification of both the system failure potential and the multi-faceted failure consequences, which affect further systems. Modern industries (including the engineering and financial sectors) require increasingly large and complex models to quantify risks that are not confined to single disciplines but cross into possibly several other areas. Disasters such as hurricane Katrina, the Fukushima nuclear incident and the global financial crisis show how failures in technical and management systems cause consequences and further failures in technological, environmental, financial, and social systems, which are all inter-related. This requires a comprehensive multi-disciplinary understanding of all aspects of uncertainty and risk and measures for risk management, reduction, control and mitigation as well as skills in applying the necessary mathematical, modelling and computational tools for risk oriented decision-making. This complexity has to be considered in very early planning stages, for example, for the realisation of green energy or nuclear power concepts and systems, where benefits and risks have to be considered from various angles. The involved parties include engineering and energy companies, banks, insurance and re-insurance companies, state and local governments, environmental agencies, the society both locally and globally, construction companies, service and maintenance industries, emergency services, etc. The CDT is focussed on training a new generation of highly-skilled graduates in this particular area of engineering, mathematics and the environmental sciences based at the Liverpool Institute for Risk and Uncertainty. New challenges will be addressed using emerging probabilistic technologies together with generalised uncertainty models, simulation techniques, algorithms and large-scale computing power. Skills required will be centred in the application of mathematics in areas of engineering, economics, financial mathematics, and psychology/social science, to reflect the complexity and inter-relationship of real world systems. The CDT addresses these needs with multi-disciplinary training and skills development on a common mathematical platform with associated computational tools tailored to user requirements. The centre reflects this concept with three major components: (1) Development and enhancement of mathematical and computational skills; (2) Customisation and implementation of models, tools and techniques according to user requirements; and (3) Industrial and overseas university placements to ensure industrial and academic impact of the research. This will develop graduates with solid mathematical skills applied on a systems level, who can translate numerical results into languages of engineering and other disciplines to influence end-users including policy makers. Existing technologies for the quantification and management of uncertainties and risks have yet to achieve their significant potential benefit for industry. Industrial implementation is presently held back because of a lack of multidisciplinary training and application. The Centre addresses this problem directly to realise a significant step forward, producing a culture change in quantification and management of risk and uncertainty technically as well as educationally through the cohort approach to PGR training.