  This is the first in a collection of three papers introducing the science
with an ultra-violet (UV) space telescope on an approximately 130~kg small
satellite with a moderately fast re-pointing capability and a real-time alert
communication system approved for a Czech national space mission. The mission,
called Quick Ultra-Violet Kilonova surveyor - QUVIK, will provide key follow-up
capabilities to increase the discovery potential of gravitational wave
observatories and future wide-field multi-wavelength surveys. The primary
objective of the mission is the measurement of the UV brightness evolution of
kilonovae, resulting from mergers of neutron stars, to distinguish between
different explosion scenarios. The mission, which is designed to be
complementary to the Ultraviolet Transient Astronomy Satellite - ULTRASAT, will
also provide unique follow-up capabilities for other transients both in the
near- and far-UV bands. Between the observations of transients, the satellite
will target other objects described in this collection of papers, which
demonstrates that a small and relatively affordable dedicated UV-space
telescope can be transformative for many fields of astrophysics.
