Emerging IoT applications with real-time latency constraints require new data processing systems operating at the Edge. Serverless computing offers a new compelling paradigm, where a user can execute a small application without handling the operational issues of server provisioning and resource management. Despite a variety of existing commercial and open source serverless platforms (utilizing VMs and containers), these solutions are too heavy-weight for a resource-constrained Edge systems (due to large memory footprint and high invocation time). Moreover, serverless workloads that focus on per-client, short-running computations are not an ideal fit for existing general purpose computing systems. In this paper, we present the design and implementation of Sledge -- a novel and efficient WebAssembly-based serverless framework for the Edge. Sledge is optimized for supporting unique properties of serverless workloads: the need for high density multi-tenancy, low startup time, bursty client request rates, and short-lived computations. Sledge is designed for these constraints by offering (i) optimized scheduling policies and efficient work-distribution for short-lived computations, and (ii) a light-weight function isolation model implemented using our own WebAssembly-based software fault isolation infrastructure. These lightweight sandboxes are designed to support high-density computation: with fast startup and teardown times to handle high client request rates. An extensive evaluation of Sledge with varying workloads and real-world serverless applications demonstrates the effectiveness of the designed serverless-first runtime for the Edge. Sledge supports up to 4 times higher throughput and 4 times lower latencies compared to Nuclio, one of the fastest open-source serverless frameworks.