The half-duplex (HD) multi-hop relay channel consists of a source, multiple HD relays connected in series, and a destination where links are present only between adjacent nodes. In this paper, we focus on decode-and-forward relays and assume that the links are impaired by block fading and additive white Gaussian noise. We design a new protocol which, unlike the conventional protocols for the multi-hop relay channel, does not adhere to a fixed and predefined pattern of using the transmit, receive, and silent states of the nodes. In particular, the proposed protocol selects the optimal states of the nodes and the corresponding optimal transmission rates based on the instantaneous channel state information (CSI) of the involved links in each fading block such that the achievable average rate from source to destination is maximized. To enable adaptive scheduling of the states of the nodes, the relay nodes have to be equipped with buffers for temporary storage of the information received from the preceding node. Additionally, we discuss and address two practical challenges arising in the implementation of the optimal protocol, namely the unconstrained end-to-end delay due to data buffering at the relays and the required CSI overhead. Numerical results confirm the superiority of the proposed buffer-aided protocols compared to existing multi-hop relaying protocols.