Centrality and Diversity are two important notions in Search in a generic manner. Their Roles in A.I., Machine Learning (ML), Social Networks, and Pattern Recognition are important. This book aims at clarifying these notions in terms of some of the foundational topics like search, representation, regression, ranking, clustering, optimization, and classification. Centrality and diversity have different roles in different tasks associated with AI and ML. For example, search may be generically viewed as playing an important role in • AI problem solving. Here, we represent a problem configuration as a state and we reach the goal state or final state by using appropriate search scheme. • Representation of a problem configuration in AI, representation of a data point, class, or cluster. • Optimization which itself involves the search for an appropriate solution. • Selecting a model for classification, clustering, or regression. • Search engines where the search is the most natural operation. Representation itself is an important task in a variety of tasks. Popularly representation deals with every task in AI and ML. Optimization is controlled through some regularizer to reduce the diversity in the solution space. Clustering is an important data abstraction task that is popular in ML, data mining, and pattern recognition. Classification and regression have some common characteristics and bias–variance trade-off unifies them. Ranking is important in a variety of tasks including information retrieval. Centrality and diversity play different roles in different tasks. In classification and regression, they show up in the form of variance and bias. In clustering, centroids represent clusters and diversity is essential in arriving at a meaningful partition. Diversity is essential in ranking search results, recommendations, and summarization of documents.