Evolution can be modelled by semi-directed phylogenetic networks, partially directed graphs where directed edges represent reticulate evolutionary events. In this thesis, we present a polynomial-time algorithm that can reconstruct a level-2 semi-directed phylogenetic network from its quarnets (4-leaf subnetworks). First, we find a canonical form of a network by reducing our information to merely quarnet-splits. Here, we use the blob-tree of the network found with quarnet-splits to construct the canonical form of the network. Finally, we consider quartets, which give more information about level-1 and level-2 quarnets, to refine on the canonical form.