Science with ASKAP - the Australian Square Kilometre Array Pathfinder

[ABRIDGED VERSION] 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. 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.