This thesis studies recommendation systems and considers joint sampling and learning. Sampling in recommendation systems is to obtain users' ratings on specific items chosen by the recommendation platform, and learning is to infer the unknown ratings of users to items given the existing data. In this thesis, the problem is formulated as an adaptive matrix completion problem in which sampling is to reveal the unknown entries of a $U\times M$ matrix where $U$ is the number of users, $M$ is the number of items, and each entry of the $U\times M$ matrix represents the rating of a user to an item. In the literature, this matrix completion problem has been studied under a static setting, i.e., recovering the matrix based on a set of partial ratings. This thesis considers both sampling and learning, and proposes an adaptive algorithm. The algorithm adapts its sampling and learning based on the existing data. The idea is to sample items that reveal more information based on the previous sampling results and then learn based on clustering. Performance of the proposed algorithm has been evaluated using simulations.