Stellar physics and evolution calculations enable a broad range of research in astrophysics. Modules for Experiments in Stellar Astrophysics (MESA) is a suite of open source libraries for a wide range of applications in computational stellar astrophysics. A newly designed 1-D stellar evolution module, MESA star, combines many of the numerical and physics modules for simulations of a wide range of stellar evolution scenarios ranging from very-low mass to massive stars, including advanced evolutionary phases. MESA star solves the fully coupled structure and composition equations simultaneously. It uses adaptive mesh refinement and sophisticated timestep controls, and supports shared memory parallelism based on OpenMP. Independently usable modules provide equation of state, opacity, nuclear reaction rates, and atmosphere boundary conditions. Each module is constructed as a separate Fortran 95 library with its own public interface. Examples include comparisons to other codes and show evolutionary tracks of very low mass stars, brown dwarfs, and gas giant planets; the complete evolution of a 1 Msun star from the pre-main sequence to a cooling white dwarf; the Solar sound speed profile; the evolution of intermediate mass stars through the thermal pulses on the He-shell burning AGB phase; the interior structure of slowly pulsating B Stars and Beta Cepheids; evolutionary tracks of massive stars from the pre-main sequence to the onset of core collapse; stars undergoing Roche lobe overflow; and accretion onto a neutron star.