This report presents the details of the governing equations, physical parameterizations, and numerical algorithms defining the version of the NCAR Community Atmosphere Model designated CAM 3.0. The material provides an overview of the major model components, and the way in which they interact as the numerical integration proceeds. Details on the coding implementation, along with in-depth information on running the CAM 3.0 code, are given in a separate technical report entitled ``User's Guide to NCAR CAM 3.0'' [96]. As before, it is our objective that this model provide NCAR and the university research community with a reliable, well documented atmospheric general circulation model. This version of the CAM 3.0 incorporates significant improvements to the physics package (e.g. generalized cloud overlap for radiation calculations), new capabilities such as the incorporation of thermodynamic sea ice, and a number of enhancements to the implementation (e.g. clean separation between physics and dynamics). We believe that collectively these improvements provide the research community with a significantly improved atmospheric modeling capability.