MathOptInterface.jl is a Julia library providing a standardized abstraction layer for mathematical optimization. It defines a common interface for formulating optimization problems (variables, constraints, objectives) and communicating with solvers. The architecture is highly modular, with core types for functions and sets, a powerful bridge system that automatically transforms constraints into solver-supported forms, file format readers/writers (MPS, LP, NL, SDPA, CBF, MOF), and utilities for model management, copying, and automatic differentiation of nonlinear expressions. The package serves as the foundation for higher-level modeling systems like JuMP and is used by dozens of optimization solvers in Julia.