Cohesion and coupling are considered amongst the most important properties to evaluate the quality of a design. In the context of OO software development, cohesion means relatedness of the public functionality of a class whereas coupling stands for the degree of dependence of a class on other classes in OO system. In this thesis, a new metric has been proposed that measures the class cohesion on the basis of relative relatedness of the public methods to the overall public functionality of a class. The proposed metric for class cohesion uses a new concept of subset tree to determine relative relatedness of the public methods to the overall public functionality of a class. A set of metrics has been proposed for measuring class coupling based on three types of UML relationships, namely association, inheritance and dependency. The reasonable metrics to measure cohesion and coupling are supposed to share the same set of input data. Sharing of input data by the metrics encourages the idea for the existence of mutual relationships between them. Based on potential relationships research questions have been formed. An attempt is made to find answers of these questions with the help of an experiment on OO system FileZilla. Mutual relationships between class cohesion and class coupling have been analyzed statistically while considering OO metrics for size and reuse. Relationships among the pairs of metrics have been discussed and results are drawn in accordance with observed correlation coefficients. A study on Software evolution with the help of class cohesion and class coupling metrics has also been performed and observed trends have been analyzed.