Hyper Suprime-Cam (HSC) is a wide-field imaging camera on the prime focus of the 8.2-m Subaru telescope on the summit of Mauna Kea in Hawaii. A team of scientists from Japan, Taiwan, and Princeton University is using HSC to carry out a 300-night multi-band imaging survey of the high-latitude sky. The survey includes three layers: the Wide layer will cover 1400 deg2 in five broad bands (grizy), with a 5 σ point-source depth of r ≈ 26. The Deep layer covers a total of 26 deg2 in four fields, going roughly a magnitude fainter, while the UltraDeep layer goes almost a magnitude fainter still in two pointings of HSC (a total of 3.5 deg2). Here we describe the instrument, the science goals of the survey, and the survey strategy and data processing. This paper serves as an introduction to a special issue of the Publications of the Astronomical Society of Japan, which includes a large number of technical and scientific papers describing results from the early phases of this survey.