This paper introduces PDEformer, a neural solver for partial differential equations (PDEs) that can handle various types of PDEs simultaneously. The model represents the PDE in the form of a computational graph, integrating both symbolic and numerical information. A graph Transformer and an implicit neural representation (INR) are used to generate mesh-free predicted solutions. After pretraining on diverse PDEs, PDEformer achieves zero-shot accuracies on benchmark datasets comparable to expert models trained specifically for individual PDEs. Additionally, it demonstrates promising results in the inverse problem of PDE coefficient recovery. The paper details the methodology, including the construction of the computational graph, encoding and decoding processes, and experimental setup. Results show that PDEformer outperforms baseline models in forward problems and effectively recovers PDE coefficients in the inverse problem, even under noisy conditions.This paper introduces PDEformer, a neural solver for partial differential equations (PDEs) that can handle various types of PDEs simultaneously. The model represents the PDE in the form of a computational graph, integrating both symbolic and numerical information. A graph Transformer and an implicit neural representation (INR) are used to generate mesh-free predicted solutions. After pretraining on diverse PDEs, PDEformer achieves zero-shot accuracies on benchmark datasets comparable to expert models trained specifically for individual PDEs. Additionally, it demonstrates promising results in the inverse problem of PDE coefficient recovery. The paper details the methodology, including the construction of the computational graph, encoding and decoding processes, and experimental setup. Results show that PDEformer outperforms baseline models in forward problems and effectively recovers PDE coefficients in the inverse problem, even under noisy conditions.