Estimation of variance components in mixed linear models is an important problem in statistical inference to draw a valid and meaningful interpretation in many practical areas of research. ANOVA, Analogous to ANOVA, SS Approach, ML, REML, MML, MINQUE, MIVQUE and QLSE are some of the important methods available in literature for estimation of variance components in general mixed linear models. In this book we have introduced MTE, WQLSE and modified MIVQUE estimators and also derived their variances and also the covariance matrices. In fact we have presented the explicit computable expressions for the computation of MTE, WQLSE, Modified MIVQUE estimators and their covariance matrices. The relative performance of MTE, QLSE, WQLSE, MIVQUE and Modified MIVQUE estimators are assessed by numerical evaluations based on different optimality criteria like T-Optimality, D-Optimality and M-Optimality together with their variances for various n-patterns. I hope that this book may be a useful guide for the applied workers to solve their practical problems and a reference book for the researchers to do research in variance components estimation.