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This paper presents optimum multi-hop transmission strategies (MHTS) for energy constrained wireless sensor networks (WSNs). Nodes in a multi-hop WSN need to transmit their own information and to relay each other's information to a base station (BS), and there are usually multiple available paths between a node and the BS. The optimum MHTS derived in this paper answers three questions: 1) how should a node divide its limited energy between the transmission of the self-information and the relay-information? 2) whether a single path or a combination of multiple paths should be used to route the information from a node to the BS? and 3) if multi-path routing is used, how should a single data stream be divided among the multiple paths? The answers to these questions are obtained by minimizing the energy per bit, or equivalently, by maximizing the amount of information delivered to the BS under certain energy constraints. Two different scheduling strategies are considered, the fair equal information strategy that requires all the nodes deliver the same amount of information to the BS, and the unfair maximum information strategy that maximizes the total amount of information delivered to the BS. The optimum MHTS for these two strategies are derived, with either convex optimization or analytical expressions, under a per node energy constraint and a total energy constraint, respectively.