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.