This book covers three topics: modelling, valuation and risk management of a rather complex financial derivative, i.e. collateralised debt obligations (CDOs). It is a financial product that takes targeted risk for the purpose of achieving targeting returns. CDOs fall into the class of credit risk derivatives. The first five chapters give an introduction to debt obligations, their mathematical modelling and valuation. Credit indices as well as valuation of default baskets are treated here. Valuation and the mechanism of synthetic CDOs together with market considerations are discoursed in Chapters 6 and 7. The following chapters (8 to 14) deal with risk quantification, extensions of the standard market model, exotic CDOs, portfolio analysis and simulation methods for hedging strategies. Some of the methods are well illustrated on cases from the real financial world. Despite the complexity of the financial instrument in question, the mathematics used for modelling and analysing the phenomena is of college level and therefore understandable to a wide community of potential readers. The book can be highly recommended for financial mathematicians and financial analysts.