This is a book about the modelling, valuation and risk management of synthetic collateralised debt obligations (or synthetic CDOs or simply CDOs for short). Synthetic CDOs are an example of a structured credit product. This is a financial product that takes targeted risk for the purpose of achieving targeted returns. Structured credit products utilise two financial engineering technologies: credit derivatives and asset securitisation. Synthetic CDOs have played an increasingly important role in the expansion of the global credit derivatives market which has grown rapidly since the turn of the century. Indeed, it is estimated that by the end of 2006 the total credit derivative notional amount outstanding was over $20 trillion (from virtually zero only a decade earlier). Increased trading volumes naturally led to market participants becoming more sophisticated (in terms of their risk/return characteristics and the strategies they employ) as well as to a commensurate increase in the complexity and subtlety of the products available. This in turn drives the evolution of the mathematical and computational models used to value these products. The objective of this book is to collate, summarise and critically assess the current state-of-the-art in quantitative and computational modelling of synthetic CDOs. The key word here is modelling; the book is about mathematical models and their properties. This book is not intended to provide detailed descriptions of the business and economic rationales for trading credit derivatives; there are better resources available that describe this and due reference will be given to these sources.