Representing scenes with multiple semi-transparent colored layers has been a popular and successful choice for real-time novel view synthesis. Existing approaches infer colors and transparency values over regularly-spaced layers of planar or spherical shape. In this work, we introduce a new view synthesis approach based on multiple semi-transparent layers with scene-adapted geometry. Our approach infers such representations from stereo pairs in two stages. The first stage infers the geometry of a small number of data-adaptive layers from a given pair of views. The second stage infers the color and the transparency values for these layers producing the final representation for novel view synthesis. Importantly, both stages are connected through a differentiable renderer and are trained in an end-to-end manner. In the experiments, we demonstrate the advantage of the proposed approach over the use of regularly-spaced layers with no adaptation to scene geometry. Despite being orders of magnitude faster during rendering, our approach also outperforms a recently proposed IBRNet system based on implicit geometry representation. See results at https://samsunglabs.github.io/StereoLayers .