To study galaxies during the cosmic era of maximum star formation and supermassive black hole growth requires observing them at great distances, corresponding to cosmological redshifts between 1.5 and 3.0. The visible light emitted by these galaxies carries information about their stellar and gaseous contents; owing to the redshift, this light is observed at infrared wavelengths. The new, NSF-funded, Multi-Object Spectrometer for Infra-Red Exploration (MOSFIRE) on the Keck I telescope represents a major development for the study of these galaxies, offering increases in sensitivity and survey efficiency by factors of approximately 5 and 100, respectively. This project, the MOSFIRE Deep Evolution Field (MOSDEF) Survey, will chart the evolution of the rest-frame optical spectra for approximately 2000 galaxies between 1.5 and 3.5, more than an order of magnitude improvement over existing surveys. The project will make use of 44 nights allocated on the Keck I telescope through 2016, and will survey three well-studied regions of the sky already having extensive multi-wavelength datasets. By combining new and existing data, the proposing team will characterize the star formation and accreting black hole activity in distant galaxies, their masses, contents and structures, and the manner in which baryonic matter passes through them. In collaboration with theorists, the MOSDEF team will use these results to test and inform forefront models of galaxy evolution. The MOSDEF spectra will be publicly released to the astronomical community to enable additional investigations. Graduate and undergraduate students will be supported by the project and involved in the research, and team members will develop pedagogical resources for K-12 teachers on the key aspects of the science and techniques.