In the Present Book Chapter - I is an introductory one. It contains the general introduction about the problem of testing linear restrictions on the parameters of the linear regression models, Chapter - II describes the concept and the estimation of parameters of linear model subject to the linear restrictions. Chapter - III deals with the review about the various tests for linear restrictions in the linear statistical models including Wald, Likelihood Ratio and Lagrange Multiplier tests. Chapter - IV gives the details about the various problems of testing equality between sets of regression coefficients in linear regression models, Chapter - V proposes some new criteria for testing linear restrictions on parameters in linear statistical models. Chapter - VI presents the conclusions. Several selected references for the present research work have been given under the title "BIBLIOGRAPHY."