This document introduces the exciting and fundamentally new science and astronomy that the European New Gravitational Wave Observatory (NGO) mission (derived from the previous LISA proposal) will deliver. The mission (which we will refer to by its informal name ``eLISA) will survey for the first time the low-frequency gravitational wave band (about 0:1 mHz to 1 Hz), with sufficient sensitivity to detect interesting individual astrophysical sources out to z = 15. The measurements described here will address the basic scientific goals that have been captured in ESAs ``New Gravitational Wave Observatory Science Requirements Document; they are presented here so that the wider scientific community can have access to them. The eLISA mission will ...