This article describes a 2D and 3D adaptive and mass conservingsemi-Lagrangian advection scheme for atmospheric transport problems. Fromthe integral form of the conservation law we derive a semi-Lagrangian schemebased on conservation of mass along trajectories. The mapping of mass fromthe old (adaptively refined and possibly different) grid to the upstream controlvolume is performed by a mass packet based scheme, essentially consistingof a sub-grid discretization. We validate the new adaptive and conservativesemi-Lagrangian scheme with four different analytic test cases.