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Enclosing problem is an important area of algorithmic research in computer science community which arise in facility location. Due to some constraints, it is not always possible to meet the demand of each client/customer. This constraint gives the birth of the maximal enclosing problem. This book considers the maximal enclosing problem using one and two axis-parallel unit square(s). Then the k-enclosing problem using an axis-parallel square is considered as an extension of the maximal enclosing problem. This book concludes with some future directions of research.