CasADi is an open-source software framework for numerical optimization and optimal control. It offers a flexible and efficient tool for modeling and solving optimization problems, with a focus on problems constrained by differential equations, such as optimal control problems. CasADi is written in self-contained C++ but is most conveniently used via interfaces to Python, MATLAB, or Octave. Since its inception in 2009, it has been used in academic teaching and various applications, including process control, robotics, and aerospace. The framework provides a set of general-purpose building blocks that significantly reduce the effort needed to implement algorithms for numerical optimal control without sacrificing efficiency. CasADi is suitable for teaching optimal control to graduate students and allows researchers and practitioners to write customized code for specific applications. CasADi's symbolic core includes a state-of-the-art implementation of algorithmic differentiation (AD), enabling automatic sensitivity analysis for ODEs and DAEs. It supports both forward and reverse modes of AD, allowing efficient calculation of derivatives. The framework also provides a common interface for formulating optimization problems, such as nonlinear programs (NLPs), linear programs (LPs), and quadratic programs (QPs), and delegates numerical solution to third-party solvers. CasADi's symbolic framework allows users to construct expressions and define automatically differentiable functions. It supports two expression types: SX for scalar expressions and MX for matrix expressions. The framework uses a directed acyclic graph (DAG) representation for expressions, enabling efficient numerical evaluation and derivative calculations. CasADi also supports C code generation and just-in-time compilation, allowing for high-performance execution on embedded systems. CasADi supports implicit differentiable functions, including solutions to linear and nonlinear systems of equations, initial-value problems in ODEs and DAEs, and integrators for optimal control problems. It provides a plugin-based architecture for solving optimization problems, with support for various solvers, including open-source and commercial tools. The framework is designed to handle sparse and structured problems efficiently, with a focus on large-scale optimization and sensitivity analysis. CasADi's ability to calculate derivatives to any order and its support for mixed-integer formulations make it a versatile tool for a wide range of applications in optimization and optimal control.CasADi is an open-source software framework for numerical optimization and optimal control. It offers a flexible and efficient tool for modeling and solving optimization problems, with a focus on problems constrained by differential equations, such as optimal control problems. CasADi is written in self-contained C++ but is most conveniently used via interfaces to Python, MATLAB, or Octave. Since its inception in 2009, it has been used in academic teaching and various applications, including process control, robotics, and aerospace. The framework provides a set of general-purpose building blocks that significantly reduce the effort needed to implement algorithms for numerical optimal control without sacrificing efficiency. CasADi is suitable for teaching optimal control to graduate students and allows researchers and practitioners to write customized code for specific applications. CasADi's symbolic core includes a state-of-the-art implementation of algorithmic differentiation (AD), enabling automatic sensitivity analysis for ODEs and DAEs. It supports both forward and reverse modes of AD, allowing efficient calculation of derivatives. The framework also provides a common interface for formulating optimization problems, such as nonlinear programs (NLPs), linear programs (LPs), and quadratic programs (QPs), and delegates numerical solution to third-party solvers. CasADi's symbolic framework allows users to construct expressions and define automatically differentiable functions. It supports two expression types: SX for scalar expressions and MX for matrix expressions. The framework uses a directed acyclic graph (DAG) representation for expressions, enabling efficient numerical evaluation and derivative calculations. CasADi also supports C code generation and just-in-time compilation, allowing for high-performance execution on embedded systems. CasADi supports implicit differentiable functions, including solutions to linear and nonlinear systems of equations, initial-value problems in ODEs and DAEs, and integrators for optimal control problems. It provides a plugin-based architecture for solving optimization problems, with support for various solvers, including open-source and commercial tools. The framework is designed to handle sparse and structured problems efficiently, with a focus on large-scale optimization and sensitivity analysis. CasADi's ability to calculate derivatives to any order and its support for mixed-integer formulations make it a versatile tool for a wide range of applications in optimization and optimal control.