In this letter we present SA-CNN, a hierarchical and lightweight self-attention based encoding and decoding architecture for representation learning of point cloud data. The proposed SA-CNN introduces convolution and transposed convolution stacks to capture and generate contextual information among unordered 3D points. Following conventional hierarchical pipeline, the encoding process extracts feature in local-to-global manner, while the decoding process generates feature and point cloud in coarse-to-fine, multi-resolution stages. We demonstrate that SA-CNN is capable of a wide range of applications, namely classification, part segmentation, reconstruction, shape retrieval, and unsupervised classification. While achieving the state-of-the-art or comparable performance in the benchmarks, SA-CNN maintains its model complexity several order of magnitude lower than the others. In term of qualitative results, we visualize the multi-stage point cloud reconstructions and latent walks on rigid objects as well as deformable non-rigid human and robot models.