  We present the first catalogue of galaxy cluster candidates derived from the
third data release of the Kilo Degree Survey (KiDS-DR3). The sample of clusters
has been produced using the Adaptive Matched Identifier of Clustered Objects
(AMICO) algorithm. In this analysis AMICO takes advantage of the luminosity and
spatial distribution of galaxies only, not considering colours. In this way, we
prevent any selection effect related to the presence or absence of the
red-sequence in the clusters. The catalogue contains 7988 candidate galaxy
clusters in the redshift range 0.1<z<0.8 down to S/N>3.5 with a purity
approaching 95% over the entire redshift range. In addition to the catalogue of
galaxy clusters we also provide a catalogue of galaxies with their
probabilistic association to galaxy clusters. We quantify the sample purity,
completeness and the uncertainties of the detection properties, such as
richness, redshift, and position, by means of mock galaxy catalogues derived
directly from the data. This preserves their statistical properties including
photo-z uncertainties, unknown absorption across the survey, missing data,
spatial correlation of galaxies and galaxy clusters. Being based on the real
data, such mock catalogues do not have to rely on the assumptions on which
numerical simulations and semi-analytic models are based on. This paper is the
first of a series of papers in which we discuss the details and physical
properties of the sample presented in this work.
