Q uantile regression ( QR) was introduced as an extension of the dir=ltr On the other hand, d ependent data arise in many studies. Frequently adopted sampling designs, such as cluster and repeated measures, may induce this dependence, which the analysis of the data needs to take into due account. T his sampling designs typically require the application of statistical methods that allow for the correlation between observations that belong to the same unit or cluster. Mixed effects models, also known random-effects models, represent highly popular and flexible models to analyze complex data. A longitudinal survey is a correlational research study that involves repeated observations of the same variables over long periods of time, often many decades. It is often a type of observational study, although they can also be structured as longitudinal randomized experiments. In longitudinal studies, the primary goal is to characterize the change in response over time and the factors that influence change. Factors can affect not only the location but also more generally the shape of the distribution of the response over time. To make inference about the shape of a population distribution, the widely popular mixed-effects regression, for example, would be inadequate, if the distribution is not approximately Gaussian. We will stud y a novel linear model for quantile regression that includes random effects in order to account for the dependence between serial observations on the same subject. The notion of QR is synonymous with robust analysis of the conditional distribution of the response variable. In order to meet the aforementioned needs, quantile regression is introduced for longitudinal and clustered data, or more generally for more complex structures of mixed effects models. In this thesis, we present a likelihood-based approach to the estimation of the linear quantile mixed models that uses the asymmetric Laplace density. The approach hinged upon the link existing between the minimization of weighted absolute deviations, typically used in quantile regression, and the maximization of a Laplace likelihood. In this thesis, it will be fully explained how linear quantile regression is fitted and how its parameters are estimated. then deals with the fitting quantile regression for longitudinal data and estimation and interpretation of its parameters and finally, the aforementioned model will be fitted under the linear quantile mixed models for more complex structures of mixed effects models in a more general manner. Moreover, for better understanding of the mentioned subjects, the models under study will be examined in more detail by simulating the required conditions and finally, the models will be examined practically by providing an example.