A novel higher-level flavour tagging algorithm called DL1 has been developed using a neural network at the ATLAS experiment~\cite{ATLASdetector} at the CERN Large Hadron Collider (LHC). We have investigated the potential of Deep Learning in flavour tagging using inputs from lower-level taggers. A systematic grid search over architectures and the training hyperparameter space is presented. In this novel neural network approach, the training is performed on multiple output nodes, which provides a highly flexible tagger. The DL1 studies presented show that the obtained neural network improves discrimination against both light-flavour-jets and $c$-jets, and also provides a better performing $c$-tagger. The performance for arbitrary background mixtures can be adjusted after the training according to the to the needs of the physics analysis. The resulting DL1 tagger is described and a detailed set of performance plots presented, obtained from simulated $t\overline{t}$ events at $\sqrt(s)$=13 TeV and the Run-2 data taking conditions where this tagger will be applied.