ASPECT (Advanced Solver for Problems in Earth's ConvecTion) is a massively parallel, finite-element geodynamics simulation code built on the deal.II library. It solves the Stokes and advection-diffusion equations for mantle convection, lithosphere dynamics, melt migration, and related tectonic processes. The code features a highly modular plugin architecture with registration macros for material models, heating models, boundary conditions, postprocessors, mesh refinement, particle tracking, and more. It includes an extensive benchmark suite for code verification and numerous cookbooks demonstrating real geodynamic applications. The repository also bundles the Geodynamic World Builder (contrib/world_builder), a standalone library for constructing initial temperature, composition, and velocity fields from structured input files. ASPECT is actively developed with continuous integration, Docker support, and coupling to external tools like Landlab and FastScape for surface processes.