An induced matching in a graph of $ G $ is a subset $ I $ of the edges of $ G $ such that the induced graph over the vertices of $ I $ is a matching ( a $ 1 $ -factor ) . In $ 1982 $ , Stockmeyer and Vazirani showed that in general, the problem of finding the maximum induced matching is an NP-complete problem. Therefore, an efficient exact algorithm to solve the problem is unlikely to exist. I n this thesis, we will go through exact and approximation algorithms to find the maximum induced matching and examine the best algorithms available to solve this problem in different modes. W e surv ey some of the exact algorithms presented to find the maximum induced matching for some specific classes of graphs. The subject has greatly stimulated interest in the combinatorics community. Further incentive to study the induced matching was made from the concept of strong coloring of graphs . In a strong coloring of a graph, each color class is an induced matching. Indeed, we call an edge coloring a strong coloring , whenever the edges of the same color form an induced matching in $ G $ . Strong coloring was first defined by Fouquet and Jolivet . Induced matching is important from both theoretical and practical aspects. There is a direct link between the maximum size of the induced matching and the i rredundancy number of a graph .