Normal-form games (NFGs) are the fundamental model of strategic interaction. We study their representation using neural networks. We describe the inherent equivariance of NFGs --- any permutation of strategies describes an equivalent game --- as well as the challenges this poses for representation learning. We then propose the NfgTransformer architecture that leverages this equivariance, leading to state-of-the-art performance in a range of game-theoretic tasks including equilibrium-solving, deviation gain estimation and ranking, with a common approach to NFG representation. We show that the resulting model is interpretable and versatile, paving the way towards deep learning systems capable of game-theoretic reasoning when interacting with humans and with each other.