This paper presents a novel framework named Point Cloud Transformer (PCT) for point cloud learning. PCT is based on the Transformer architecture, which has achieved significant success in natural language processing and shows great potential in image processing. It is inherently permutation invariant for processing a sequence of points, making it well-suited for point cloud learning. To better capture local context within the point cloud, the input embedding is enhanced with the support of farthest point sampling and nearest neighbor search. Extensive experiments demonstrate that PCT achieves state-of-the-art performance on shape classification, part segmentation, semantic segmentation, and normal estimation tasks. The key idea of PCT is using the inherent order invariance of Transformer to avoid the need to define the order of point cloud data and conduct feature learning through the attention mechanism. The PCT framework includes a coordinate-based input embedding module, an optimized offset-attention module, and a neighbor embedding module. These adjustments make PCT more suitable for point cloud feature learning and achieve state-of-the-art performance on various tasks. The PCT framework is evaluated on two public datasets, ModelNet40 and ShapeNet, and shows superior performance compared to other methods. It achieves high accuracy in classification, normal estimation, and part segmentation tasks. The PCT framework is also efficient in terms of computational requirements, making it suitable for deployment on mobile devices. The encoder-decoder structure of Transformer supports more complex tasks, such as point cloud generation and completion. The PCT framework is extended to further applications, and more precise methods are attempted to approximate Laplacian operation and complete offset-attention.This paper presents a novel framework named Point Cloud Transformer (PCT) for point cloud learning. PCT is based on the Transformer architecture, which has achieved significant success in natural language processing and shows great potential in image processing. It is inherently permutation invariant for processing a sequence of points, making it well-suited for point cloud learning. To better capture local context within the point cloud, the input embedding is enhanced with the support of farthest point sampling and nearest neighbor search. Extensive experiments demonstrate that PCT achieves state-of-the-art performance on shape classification, part segmentation, semantic segmentation, and normal estimation tasks. The key idea of PCT is using the inherent order invariance of Transformer to avoid the need to define the order of point cloud data and conduct feature learning through the attention mechanism. The PCT framework includes a coordinate-based input embedding module, an optimized offset-attention module, and a neighbor embedding module. These adjustments make PCT more suitable for point cloud feature learning and achieve state-of-the-art performance on various tasks. The PCT framework is evaluated on two public datasets, ModelNet40 and ShapeNet, and shows superior performance compared to other methods. It achieves high accuracy in classification, normal estimation, and part segmentation tasks. The PCT framework is also efficient in terms of computational requirements, making it suitable for deployment on mobile devices. The encoder-decoder structure of Transformer supports more complex tasks, such as point cloud generation and completion. The PCT framework is extended to further applications, and more precise methods are attempted to approximate Laplacian operation and complete offset-attention.