  We propose a space-based interferometer surveying the gravitational wave (GW)
sky in the milli-Hz to $\mu$-Hz frequency range. By the 2040s', the $\mu$-Hz
frequency band, bracketed in between the Laser Interferometer Space Antenna
(LISA) and pulsar timing arrays, will constitute the largest gap in the
coverage of the astrophysically relevant GW spectrum. Yet many outstanding
questions related to astrophysics and cosmology are best answered by GW
observations in this band. We show that a $\mu$-Hz GW detector will be a truly
overarching observatory for the scientific community at large, greatly
extending the potential of LISA. Conceived to detect massive black hole
binaries from their early inspiral with high signal-to-noise ratio, and
low-frequency stellar binaries in the Galaxy, this instrument will be a
cornerstone for multimessenger astronomy from the solar neighbourhood to the
high-redshift Universe.
