A very rigorous and advanced next-generation neutronics design system, AEGIS (Anisotropic, Extended Geometry, Integrated Neutronics Solver), which is based on the deterministic method, is being developed using advanced computer science technology. The method of characteristics, which has the merit of treating heterogeneous geometry explicitly, is utilized in AEGIS as a neutron transport solver. So, the AEGIS code can explicitly model many types of fuel lattices in both commercial light water reactors (LWRs) and advanced reactors such as Generation IV reactors. The AEGIS code can also treat higher-order anisotropic scattering accurately based on spherical harmonics expansion. To compute a large-scale problem, a nonuniform ray-tracing method is implemented in AEGIS. It utilizes the Gauss-Legendre quadrature weight and the macroband method to decide position and width of ray traces to reduce spatial discretization error efficiently. The transport solution of AEGIS has been verified through various benchmark problems. It was found that the AEGIS code can explicitly treat complicated geometry and can efficiently solve a large-scale problem. These results show that flexibility in handling geometry and the very rigorous neutronics calculation models of AEGIS will contribute to predicting neutronics characteristics accurately, not only for commercial LWRs but also for advanced reactors.