A Peer-to-Peer (P2P) network is a dynamic collection of nodes that connect with each other via virtual overlay links built upon an underlying network (usually, the Internet). P2P networks are highly dynamic and can experience very heavy churn, i.e., a large number of nodes join/leave the network continuously. Thus, building and maintaining a stable overlay network is an important problem that has been studied extensively for two decades. In this paper, we present our \Pe overlay network called Sparse Robust Addressable Network (Spartan). Spartan can be quickly and efficiently built in a fully distributed fashion within $O(\log n)$ rounds. Furthermore, the Spartan overlay structure can be maintained, again, in a fully distributed manner despite adversarially controlled churn (i.e., nodes joining and leaving) and significant variation in the number of nodes. Moreover, new nodes can join a committee within $O(1)$ rounds and leaving nodes can leave without any notice. The number of nodes in the network lies in $[n, fn]$ for any fixed $f\ge 1$. Up to $εn$ nodes (for some small but fixed $ε> 0$) can be adversarially added/deleted within {\em any} period of $P$ rounds for some $P \in O(\log \log n)$. Despite such uncertainty in the network, Spartan maintains $Θ(n/\log n)$ committees that are stable and addressable collections of $Θ(\log n)$ nodes each for $O(polylog(n))$ rounds with high probability. Spartan's committees are also capable of performing sustained computation and passing messages between each other. Thus, any protocol designed for static networks can be simulated on Spartan with minimal overhead. This makes Spartan an ideal platform for developing applications. We experimentally show that Spartan will remain robust as long as each committee, on average, contains 24 nodes for networks of size up to $10240$.