In this paper, we present a learning-based approach to determining acceptance of arguments under several abstract argumentation semantics. More specifically, we propose an argumentation graph neural network (AGNN) that learns a message-passing algorithm to predict the likelihood of an argument being accepted. The experimental results demonstrate that the AGNN can almost perfectly predict the acceptability under different semantics and scales well for larger argumentation frameworks. Furthermore, analysing the behaviour of the message-passing algorithm shows that the AGNN learns to adhere to basic principles of argument semantics as identified in the literature, and can thus be trained to predict extensions under the different semantics – we show how the latter can be done for multi-extension semantics by using AGNNs to guide a basic search. We publish our code at https://github.com/DennisCraandijk/DL-Abstract-Argumentation.