We present HandAvatar, a novel representation for hand animation and rendering, which can generate smoothly compositional geometry and self-occlusion-aware texture. Specifically, we first develop a MANO-HD model as a high-resolution mesh topology to fit personalized hand shapes. Sequentially, we decompose hand geometry into per-bone rigid parts, and then re-compose paired geometry encodings to derive an across-part consistent occupancy field. As for texture modeling, we propose a self-occlusion-aware shading field (SelF). In SelF, drivable anchors are paved on the MANO-HD surface to record albedo information under a wide variety of hand poses. Moreover, directed soft occupancy is designed to describe the ray-to-surface relation, which is leveraged to generate an illumination field for the disentanglement of pose-independent albedo and pose-dependent illumination. Trained from monocular video data, our HandAvatar can perform free-pose hand animation and rendering while at the same time achieving superior appearance fidelity. We also demonstrate that HandAvatar provides a route for hand appearance editing.