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The use of wireless transmission networks in various environments has become widespread. One of the main challenges in wireless networks is that the wireless transmission is highly vulnerable to eavesdropping attacks. In this paper, an amplifyand-forward cooperative relaying wireless system with relay selection is considered to improve the physical layer (PHY) security of the wireless system in the presence of multiple eavesdroppers, under two cases, namely, perfect channel state information (CSI) and outdated CSI cases. To evaluate the PHY security of the system, we derive closed-form expressions for the PHY security performance metrics, including the probability of non-zero secrecy capacity, the average secrecy capacity, and the secrecy outage probability. Then using those expressions, we obtain several numerical results under system parameters. The results show that relay selection provides significant improvement in the PHY security of the system. Moreover, it is observed that, when the CSI used to select the best relay is outdated, the PHY secrecy performance is relatively inferior compared to that of the perfect CSI case. Finally, the obtained mathematical expressions are also validated using Monte-Carlo simulation.