Group theory which emanated from abstract algebra.Due to its abstract nature, it was seems to be an arts subject rather than a science subject. In fact it was consider pure abstract and not practical. Even students of group theory after being introduce to the course seems not to believe as to whether the subject have any practical application in real life situations because of its abstract nature. This problem prompt the researchers to study the different ways in which groups can be expressed concretely both from theoretical and practical point of view, with intention of bringing its real life application in games and puzzles for better understanding of the subject. Some popular recreational games have a group theoretic foundation which is unknown to many and some cases group helps provide strategies to win these games. Groups are useful in modelling games that involve a series of discrete moves, with each moves leading to a change in the board state. This book discuss how different facets of the definition relate with the different ways in which groups turn in games and puzzles,this work can be useful to group theorist,applied mathematician, decision making in organizations.