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This thesis contains a report of the investigations made into the mathematical aspects of inventory models with quality as the aspect for discussion. When the demand is partly influenced by quality of the items in stock, it is called Quality Dependent Demand. in chapter-2. A simple base stock system with probabilistic lead time has been used for this purpose and the quality aspect has been modeled by a 'displaced lead time distribution'. In chapter-3, the issue of using a sampling plan to accept or reject the lot on its arrival, has been discussed. A rectifying inspection procedure with non-replacement of defective items has been applied with ATI as the criterion to design the sampling plan. In chapter-4 deals with a case in which continuous monitoring of quality is required for perishable items. In chapter-5 are based on an elementary model that can explain demand in terms of quality(stock on display).