Information theory is a branch of applied Mathematics-statistics and operations Research. In the era of internet, every walk of life has been traped by the word 'Information' removal of uncertainty or entropy, Information theory includes information processing, information storage, information retrieved and decision making. In a narrow sense, information theory studies all theoritical problems concerned with the transmission of information over communication channels. This includes the studies of uncertainty (information) measure and various practical and economical methods of coding information for transmission. In this book a study of parametric R-norm Information measures, Unified (r, s) weighted information measures and their inequalities, W-majorization and some propositions connected with weighted information measures, Shannon-Gibbs type inequalities and convexities some well known inequalities like Jenson, Holder's, Minkowski's have been connected with different measures and Sub-additive measures of information has been presented.