  We present constraints on the flat $\Lambda$CDM cosmological model through a
joint analysis of galaxy abundance, galaxy clustering and galaxy-galaxy lensing
observables with the Kilo-Degree Survey. Our theoretical model combines a
flexible conditional stellar mass function, to describe the galaxy-halo
connection, with a cosmological N-body simulation-calibrated halo model to
describe the non-linear matter field. Our magnitude-limited bright galaxy
sample combines 9-band optical-to-near-infrared photometry with an extensive
and complete spectroscopic training sample to provide accurate redshift and
stellar mass estimates. Our faint galaxy sample provides a background of
accurately calibrated lensing measurements. We constrain the structure growth
parameter $S_8=\sigma_8\sqrt{\Omega_{\mathrm{m}}/0.3}=0.773^{+0.028}_{-0.030}$,
and the matter density parameter $\Omega_{\mathrm{m}}=0.290^{+0.021}_{-0.017}$.
The galaxy-halo connection model adopted in the work is shown to be in
agreement with previous studies. Our constraints on cosmological parameters are
comparable to, and consistent with, joint $3\times2{\mathrm{pt}}$
clustering-lensing analyses that additionally include a cosmic shear
observable. This analysis therefore brings attention to the significant
constraining power in the often-excluded non-linear scales for galaxy
clustering and galaxy-galaxy lensing observables. By adopting a theoretical
model that accounts for non-linear halo bias, halo exclusion, scale-dependent
galaxy bias and the impact of baryon feedback, this work demonstrates the
potential and a way forward to include non-linear scales in cosmological
analyses. Varying the width of the satellite galaxy distribution with an
additional parameter yields a strong preference for sub-Poissonian variance,
improving the goodness of fit by 0.18 in reduced $\chi^{2}$ value compared to a
fixed Poisson distribution.
