Transformer-based light field (LF) super-resolution (SR) methods have recently achieved significant performance improvements due to global feature modeling by self-attention mechanisms. However, as a method designed for natural language processing, 4D LFs are reshaped into 1D sequences with an immense set of tokens, which results in a quadratic computational complexity cost. In this paper, a spatial–angular–epipolar swin transformer (SAEST) is proposed for spatial and angular SR (SASR), which sufficiently extracts SR information in the spatial, angular, and epipolar domains using local self-attention with shifted windows. Specifically, in SAEST, a spatial swin transformer and an angular standard transformer are firstly cascaded to extract spatial and angular SR features, separately. Then, the extracted SR feature is reshaped into the epipolar plane image pattern and fed into an epipolar swin transformer to extract the spatial–angular correlation information. Finally, several SAEST blocks are cascaded in a Unet framework to extract multi-scale SR features for SASR. Experiment results indicate that SAEST is a fast transformer-based SASR method with less running time and GPU consumption and has outstanding performance on simulated and real-world public datasets.