  The coldest and densest structures of gas and dust in the Universe have
unique spectral signatures across the (sub-)millimetre bands ($\nu \approx
30-950$~GHz). The current generation of single dish facilities has given a
glimpse of the potential for discovery, while sub-mm interferometers have
presented a high resolution view into the finer details of known targets or in
small-area deep fields. However, significant advances in our understanding of
such cold and dense structures are now hampered by the limited sensitivity and
angular resolution of our sub-mm view of the Universe at larger scales.
  In this context, we present the case for a new transformational astronomical
facility in the 2030s, the Atacama Large Aperture Submillimetre Telescope
(AtLAST). AtLAST is a concept for a 50-m-class single dish telescope, with a
high throughput provided by a 2~deg - diameter Field of View, located on a
high, dry site in the Atacama with good atmospheric transmission up to $\nu\sim
1$~THz, and fully powered by renewable energy.
  We envision AtLAST as a facility operated by an international partnership
with a suite of instruments to deliver the transformative science that cannot
be achieved with current or in-construction observatories. As an 50m-diameter
telescope with a full complement of advanced instrumentation, including highly
multiplexed high-resolution spectrometers, continuum cameras and integral field
units, AtLAST will have mapping speeds hundreds of times greater than current
or planned large aperture ($>$ 12m) facilities. By reaching confusion limits
below L$_*$ in the distant Universe, resolving low-mass protostellar cores at
the distance of the Galactic Centre, and directly mapping both the cold and the
hot (the Sunyaev-Zeldovich effect) circumgalactic medium of galaxies, AtLAST
will enable a fundamentally new understanding of the sub-mm Universe.
