Title Hamilton-Jacobi Equations on Lie Groupoids Type of Research Presentation Keywords Hamilton-Jacobi equations, Lie algebroids, Lie groupoids Abstract In this paper, we use some well-known results about Hamiltonian Mechanics to introduce geometric version of Hamilton-Jacobi equations on Lie algebroids and we take pair groupoid and Atiyah groupoid as special examples. Researchers Ghorbanali Haghighatdoost Bonab (First Researcher)، Rezvaneh Ayoubi (Second Researcher)