The paper introduces MESA (Modules for Experiments in Stellar Astrophysics), an open-source suite of robust and efficient libraries for computational stellar astrophysics. MESA includes a 1-D stellar evolution module, MESA star, which combines numerical and physics modules to simulate a wide range of stellar evolution scenarios, from very-low-mass to massive stars, including advanced evolutionary phases. MESA star solves coupled structure and composition equations simultaneously, using adaptive mesh refinement and sophisticated timestep controls, and supports shared memory parallelism based on OpenMP. The software is designed to be modular, with each module constructed as a separate Fortran 95 library, facilitating independent development and verification. The paper outlines the design and implementation of MESA modules, describes the numerical, microphysical, and macrophysical modules, and presents detailed examples demonstrating the capabilities of MESA, including evolutionary tracks of low-mass stars, brown dwarfs, and gas giant planets, as well as the complete evolutionary track of a 1 solar mass star from the pre-main sequence to a cooling white dwarf. MESA is available for download from the project website and is intended to engage the broader astrophysics community in testing, contributing, and sharing experience.The paper introduces MESA (Modules for Experiments in Stellar Astrophysics), an open-source suite of robust and efficient libraries for computational stellar astrophysics. MESA includes a 1-D stellar evolution module, MESA star, which combines numerical and physics modules to simulate a wide range of stellar evolution scenarios, from very-low-mass to massive stars, including advanced evolutionary phases. MESA star solves coupled structure and composition equations simultaneously, using adaptive mesh refinement and sophisticated timestep controls, and supports shared memory parallelism based on OpenMP. The software is designed to be modular, with each module constructed as a separate Fortran 95 library, facilitating independent development and verification. The paper outlines the design and implementation of MESA modules, describes the numerical, microphysical, and macrophysical modules, and presents detailed examples demonstrating the capabilities of MESA, including evolutionary tracks of low-mass stars, brown dwarfs, and gas giant planets, as well as the complete evolutionary track of a 1 solar mass star from the pre-main sequence to a cooling white dwarf. MESA is available for download from the project website and is intended to engage the broader astrophysics community in testing, contributing, and sharing experience.