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This book is based on the important contributions in model selection by Dr. M. S. Rahman and his co-authors Professor M. L. King, Dr. G. K. Bose, Dr. M. R. Laskar and Mrs. S. Nahar. We have developed an analytical formula for finding the probability of correct selection. We have proposed a new criterion named JIC based on the combination of BIC and RBAR criteria and showed that JIC performed better in most cases than all existing criteria. We have introduced generalized criterion based on residual sum of squares with a multiplicative penalty function. We have proposed improved penalty functions for information criteria-based model selection which involves the use of computer simulation methods to improve the choice of penalty function. We have also examined the effect of making a restriction on parameters of interest within a model selection framework. We have studied the relation between model selection and hypothesis testing. Marginal penalty functions are derived for all criteria and used to compare the performances of all existing criteria. It is observed that in general RBAR criterion favors the higher parametric model and BIC favors the lower parametric model.