Based on a course in the theory of statistics this text concentrates on what can be achieved using the likelihood Fisherian method of taking account of uncertainty when studying a statistical problem It takes the concept ot the likelihood as providing the best methods for unifying the demands of statistical modelling & the theory of inference Every likelihood concept is illustrated by realistic examples which are not compromised by computational problems Examples range from a simile comparison of two accident rates to complex studies that require generalised linear or semiparametric modelling The emphasis is that the likelihood is not simply a device to produce an estimate but an important tool for modelling The book generally takes an informal approach where most important results are established using heuristic arguments & motivated with realistic examples With the currently available computing power examples are not contrived to allow a closed analytical solution & the book can concentrate on the statistical aspects of the data modelling In addition to classical likelihood theory the book covers many modern topics such as generalized linear models & mixed models non parametric smoothing robustness the EM algorithm & empirical likelihood