Summary: In these lecture notes we investigate the implications of the identification of strategies with quantum operations in game theory beyond the results presented in J. Eisert, M. Wilkins and M. Lewenstein [Phys. Rev. Lett. 83, 3077-3080 (1999; Zbl 0946.81018)]. After introducing a general framework, we study quantum games with a classical analogue in order to flesh out the peculiarities of game theoretical settings in the quantum domain. Special emphasis is given to a detailed investigation of different sets of quantum strategies.