Self-supervised learning (SSL) has become prevalent for learning representations in computer vision. Notably, SSL exploits contrastive learning to encourage visual representations to be invariant under various image transformations. The task of gaze estimation, on the other hand, demands not just invariance to various appearances but also equivariance to the geometric transformations. In this work, we propose a simple contrastive representation learning framework for gaze estimation, named Gaze Contrastive Learning (GazeCLR). GazeCLR exploits multi-view data to promote equivariance and relies on selected data augmentation techniques that do not alter gaze directions for invariance learning. Our experiments demonstrate the effectiveness of GazeCLR for several settings of the gaze estimation task. Particularly, our results show that GazeCLR improves the performance of cross-domain gaze estimation and yield as high as 17.2% relative improvement. Moreover, GazeCLR framework is competitive with state-of-the-art representation learning methods for few-shot evaluation.