The future of cm and m-wave astronomy lies with the Square Kilometre Array (SKA), a telescope under development by a consortium of 17 countries. The SKA will be 50 times more sensitive than any existing radio facility. A majority of the key science for the SKA will be addressed through large-area imaging of the Universe at frequencies from 300 MHz to a few GHz. The Australian SKA Pathfinder (ASKAP) is aimed squarely in this frequency range, and achieves instantaneous wide-area imaging through the development and deployment of phase-array feed systems on parabolic reflectors. This large field-of-view makes ASKAP an unprecedented synoptic telescope poised to achieve substantial advances in SKA key science. The central core of ASKAP will be located at the Murchison Radio Observatory in inland Western Australia, one of the most radio-quiet locations on the Earth and one of the sites selected by the international community as a potential location for the SKA. Following an introductory description of ASKAP, this document contains 7 chapters describing specific science programmes for ASKAP. In summary, the goals of these programmes are as follows: - The detection of a million galaxies in atomic hydrogen emission across 75% of the sky out to a redshift of 0.2 to understand galaxy formation and gas evolution in the nearby Universe.– The detection of synchrotron radiation from 60 million galaxies to determine the evolution, formation and population of galaxies across cosmic time and enabling key cosmological tests.– The detection of polarized radiation from over 500,000 galaxies, allowing a grid of rotation measures at 10′ to explore the evolution of magnetic fields in galaxies over cosmic time.– The understanding of the evolution of the interstellar medium of our own Galaxy and the processes that drive its chemical and physical evolution.– The high-resolution imaging of intense, energetic phenomena by enlarging the Australian and global Very Long Baseline networks.– The discovery and timing of a thousand new radio pulsars.– The characterization of the radio transient sky through detection and monitoring of transient sources such as gamma ray bursts, radio supernovae and intra-day variables.The combination of location, technological innovation and scientific program will ensure that ASKAP will be a world-leading radio astronomy facility, closely aligned with the scientific and technical direction of the SKA. A brief summary chapter emphasizes the point, and considers discovery space.