This book first introduces the criterion of REstricted Maximum Likelihood (REML) for the fitting of a mixed model to data before illustrating how to apply mixed model analysis to a wide range of situations, how to estimate the variance due to each random-effect term in the model, and how to obtain and interpret Best Linear Unbiased Predictors (BLUPs) estimates of individual effects that take account of their random nature. It is intended to be an introductory guide to a relatively advanced specialised topic, and to convince the reader that mixed modelling is neither so specia.