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In this paper, we consider a simple network consisting of a source, a half-duplex decode-and-forward relay, and a destination. We propose a new relaying protocol employing adaptive link selection, i.e., in any given time slot, based on the channel state information of the source-relay and the relay-destination link a decision is made whether the source or the relay transmits. In order to avoid data loss at the relay, adaptive link selection requires the relay to be equipped with a buffer such that data can be queued until the relay-destination link is selected for transmission. We study both delay-constrained and delay-unconstrained transmission. For the delay-unconstrained case, we characterize the optimal link selection policy, derive the corresponding throughput, and develop an optimal power allocation scheme. For the delay-constrained case, we propose to starve the buffer of the relay by choosing the decision threshold of the link selection policy smaller than the optimal one and derive a corresponding upper bound on the average delay. Furthermore, we propose a modified link selection protocol which avoids buffer overflow by limiting the queue size. Our analytical and numerical results show that buffer-aided relaying with adaptive link selection achieves significant throughput gains compared to conventional relaying protocols with and without buffers where the relay employs a fixed schedule for reception and transmission.