deal.II is a general-purpose object-oriented finite element library written in C++. It provides a flexible and modular framework for simulating problems using the finite element method. The library uses advanced object-oriented techniques to separate finite element implementations into smaller, reusable components, allowing for a wide range of applications without imposing a rigid framework. It avoids computational costs associated with abstract class libraries by using efficient programming techniques. The library supports a wide range of scientific applications, programming methodologies, and algorithms. It provides abstractions for mesh geometry, finite element spaces, linear algebra, input/output, and interfaces to other software, such as visualization tools. The paper describes the design and implementation of deal.II, including its data abstractions, and presents results from applications built using the library. deal.II is designed to be a toolbox for writing finite element applications, not a solution to specific problems. It provides classes and tools for setting up a mesh, assembling linear systems, solving them, and postprocessing results. The library is organized around the concept of meshes, finite element spaces, and degrees of freedom, with a focus on modularity and flexibility. The library supports adaptive mesh refinement and coarsening, allowing for efficient simulations of complex problems. It provides a variety of finite element spaces, including continuous and discontinuous elements, and supports vector-valued elements for systems of equations. The library also includes tools for handling hanging nodes, which are necessary for maintaining consistency in finite element functions across refined meshes. deal.II includes a comprehensive set of linear algebra components for solving large sparse systems of equations. It provides efficient preconditioning methods, including Jacobi, Gauss-Seidel, and SSOR, as well as blocked versions of these methods. It also includes incomplete LU decomposition and Vanka-type preconditioners. The library has interfaces to other software, including the PETSc library for parallel linear algebra and several sparse direct solvers. It supports a wide range of mesh formats and provides tools for pre- and postprocessing, including visualization and input/output capabilities. The library is available under an open-source license and has been widely used in academic and industrial applications.deal.II is a general-purpose object-oriented finite element library written in C++. It provides a flexible and modular framework for simulating problems using the finite element method. The library uses advanced object-oriented techniques to separate finite element implementations into smaller, reusable components, allowing for a wide range of applications without imposing a rigid framework. It avoids computational costs associated with abstract class libraries by using efficient programming techniques. The library supports a wide range of scientific applications, programming methodologies, and algorithms. It provides abstractions for mesh geometry, finite element spaces, linear algebra, input/output, and interfaces to other software, such as visualization tools. The paper describes the design and implementation of deal.II, including its data abstractions, and presents results from applications built using the library. deal.II is designed to be a toolbox for writing finite element applications, not a solution to specific problems. It provides classes and tools for setting up a mesh, assembling linear systems, solving them, and postprocessing results. The library is organized around the concept of meshes, finite element spaces, and degrees of freedom, with a focus on modularity and flexibility. The library supports adaptive mesh refinement and coarsening, allowing for efficient simulations of complex problems. It provides a variety of finite element spaces, including continuous and discontinuous elements, and supports vector-valued elements for systems of equations. The library also includes tools for handling hanging nodes, which are necessary for maintaining consistency in finite element functions across refined meshes. deal.II includes a comprehensive set of linear algebra components for solving large sparse systems of equations. It provides efficient preconditioning methods, including Jacobi, Gauss-Seidel, and SSOR, as well as blocked versions of these methods. It also includes incomplete LU decomposition and Vanka-type preconditioners. The library has interfaces to other software, including the PETSc library for parallel linear algebra and several sparse direct solvers. It supports a wide range of mesh formats and provides tools for pre- and postprocessing, including visualization and input/output capabilities. The library is available under an open-source license and has been widely used in academic and industrial applications.