The murrah buffalo is the premier major milk producer breed of Indian Sub continents especially in India and Pakistan. Murrah have been extensively utilized for upgrading the local buffalo in all over India and Pakistan. Improvement in buffaloes can therefore be brought about only through selection. A major objective for buffalo breeding is to enhance milk production for higher economic return. The present study was conducted on Murrah buffaloes with following aspect To estimate variance, covariance components and genetic parameters under single and multi traits procedures. To compare estimates of parameters obtained by above procedures. To estimate best linear unbiased predictions (BLUP) values of sires/animals by above procedures and To find rank correlations among sires/animals on the basis of BLUP values. This book is valuable for animal genetics and breeding research workers, research scholars and animal breeders.