Future manufacturing will witness a shift in human-robot relationships toward collaboration, compassion, and coevolution. This will require seamless human-robot knowledge transfer. Differences in language and knowledge representation hinder the transfer of knowledge between humans and robots. Thus, a unified knowledge representation system that can be shared by humans and robots is essential. Driven by this need in a product assembly scenario, we propose the Human-Robot Shared Assembly Taxonomy (HR-SAT). With HR-SAT, any comprehensive assembly task can be represented as a knowledge graph that both humans and robots can understand. To ensure consistency in task decomposition and representation, we define the key elements of HR-SAT. HR-SAT incorporates rich assembly information and provides necessary information for diverse applications, e.g., process planning, quality checking, and human-robot collaboration. The usage and practicality of HR-SAT are demonstrated through two case studies. As a unified assembly process representation schema, HR-SAT constitutes a critical step toward seamless human-robot knowledge transfer. The specifications of HR-SAT and the two case studies are available at: https://iai-hrc.github.io/hr-sat. © 2023 The Author(s)