Dynamic spectrum access allows the unlicensed wireless users (secondary users) to dynamically access the licensed bands from legacy spectrum holders (primary users) either on an opportunistic or a cooperative basis. In this paper, we focus on cooperative spectrum sharing in a wireless network consisting of multiple primary and multiple secondary users. In particular, we study the partner-selection and resource-allocation problems within a matching theory framework, in which the primary and secondary users aim at optimizing their utilities in terms of transmission rate and power consumption. We propose a distributed algorithm to find the solution of the developed matching game that results in a stable matching between the sets of the primary and secondary users. Both analytical and numerical results show that the proposed matching model is a promising approach under which the utility functions of both primary and secondary users are maximized.