Professor Lewis has worked in the areas of geometric mechanics and geometric control theory, lately the latter more so than the former. He is a recognised expert in geometric control theory. He has written many papers on geometric control theory and geometric mechanics, and has supervised five doctoral theses in these areas. He is the author of Geometric Control of Mechanical Systems, published by Springer and dealing with the interface of his two areas of expertise. Together with Manuel de Leon and Juan-Pablo Ortega, Professor Lewis started the Journal of Geometric Mechanics as a venue for publishing research in these areas.

• 1 Introduction, motivation, and background.- 2 Topologies for spaces of vector fields.- 3 Time-varying vector fields and control systems.- 4 Presheaves and sheaves of sets of vector fields.- 5 Tautological control systems: Definitions and fundamental properties.- 6 Étalé systems.- 7 Ongoing and future work.

Professor Lewis has worked in the areas of geometric mechanics and geometric control theory, lately the latter more so than the former. He is a recognised expert in geometric control theory. He has written many papers on geometric control theory and geometric mechanics, and has supervised five doctoral theses in these areas. He is the author of Geometric Control of Mechanical Systems, published by Springer and dealing with the interface of his two areas of expertise. Together with Manuel de Leon and Juan-Pablo Ortega, Professor Lewis started the Journal of Geometric Mechanics as a venue for publishing research in these areas.

• 1 Introduction, motivation, and background.- 2 Topologies for spaces of vector fields.- 3 Time-varying vector fields and control systems.- 4 Presheaves and sheaves of sets of vector fields.- 5 Tautological control systems: Definitions and fundamental properties.- 6 Étalé systems.- 7 Ongoing and future work.

Professor Lewis has worked in the areas of geometric mechanics and geometric control theory, lately the latter more so than the former. He is a recognised expert in geometric control theory. He has written many papers on geometric control theory and geometric mechanics, and has supervised five doctoral theses in these areas. He is the author of Geometric Control of Mechanical Systems, published by Springer and dealing with the interface of his two areas of expertise. Together with Manuel de Leon and Juan-Pablo Ortega, Professor Lewis started the Journal of Geometric Mechanics as a venue for publishing research in these areas.

• 1 Introduction, motivation, and background.- 2 Topologies for spaces of vector fields.- 3 Time-varying vector fields and control systems.- 4 Presheaves and sheaves of sets of vector fields.- 5 Tautological control systems: Definitions and fundamental properties.- 6 Étalé systems.- 7 Ongoing and future work.