In most models the parameter vector can be split into two parts:the interest parameter and the nuisance parameter. The former is the focus of enquiry, while the latter summarizes aspects of the model that are not of central concern, but which are nevertheless essential to realistic modelling.Usually the interest parameter has small dimension, often being scalar, while the nuisance parameter may be of high dimension.In this lecture,we will discuss how to construct a marginal or conditional likelihood eliminating the nuisance parameter.