  As one of Stage IV space-based telescopes, China Space Station Telescope
(CSST) can perform photometric and spectroscopic surveys simultaneously to
efficiently explore the Universe in extreme precision. In this work, we
investigate several powerful CSST cosmological probes, including cosmic shear,
galaxy-galaxy lensing, photometric and spectroscopic galaxy clustering, and
number counts of galaxy clusters, and study the capability of these probes by
forecasting the results of joint constraints on the cosmological parameters. By
referring to real observational results, we generate mock data and estimate the
measured errors based on CSST observational and instrumental designs. To study
the systematical effects on the results, we also consider a number of
systematics in CSST photometric and spectroscopic surveys, such as the
intrinsic alignment, shear calibration uncertainties, photometric redshift
uncertainties, galaxy bias, non-linear effects, instrumental effects, etc. The
Fisher matrix method is used to derive the constraint results from individual
or joint surveys on the cosmological and systematical parameters. We find that
the joint constraints by including all these CSST cosmological probes can
significantly improve the results from current observations by one order of
magnitude at least, which gives $\Omega_m$ and $\sigma_8$ $<$1% accuracy, and
$w_0$ and $w_a$ $<$5% and 20% accuracies, respectively. This indicates that the
CSST photometric and spectroscopic multi-probe surveys could provide powerful
tools to explore the Universe and greatly improve the studies of relevant
cosmological problems.
