We present the Synthetic UniveRses For Surveys ({\sc surfs}) simulations, a set of N-body/Hydro simulations of the concordance $Λ$ Cold Dark Matter (\LCDM) cosmology. These simulations use Planck cosmology, contain up to 10 billion particles and sample scales & halo masses down to $1~$kpc & $10^8{\rm M}_\odot$. We identify and track haloes from $z=24$ to today using a state-of-the-art 6D halo finder and merger tree builder. We demonstrate that certain properties of halo merger trees are numerically converged for haloes composed of $\gtrsim100$ particles. Haloes smoothly grow in mass, $V_{\rm max}$, with the mass history characterised by $\log M(a)\propto\exp\left[-(a/β)^α\right]$ where $a$ is the scale factor, $α(M)\approx0.8$ \& $β(M)\approx0.024$, with these parameters decreasing with decreasing halo mass. Subhaloes follow power-law cumulative mass and velocity functions, i.e. $n(>f)\propto f^{-α}$ with $α_{M}=0.83\pm0.01$ and $α_{V_{\rm max}}=2.13\pm0.03$ for mass \& velocity respectively, independent of redshift, as seen in previous studies. The halo-to-halo scatter in amplitude is $0.9$~dex. The number of subhaloes in a halo weakly correlates with a halo's concentration $c$ \& spin $λ$:haloes of high $c$ \& low $λ$ have $60\%$ more subhaloes than similar mass haloes of low $c$ \& high $λ$. High cadence tracking shows subhaloes are dynamic residents, with $25\%$ leaving their host halo momentarily, becoming a backsplash subhalo, and another $20\%$ changing hosts entirely, in agreement with previous studies. In general, subhaloes have elliptical orbits, $e\approx0.6$, with periods of $2.3^{+2.1}_{-1.7}$~Gyrs. Subhaloes lose most of their mass at pericentric passage with mass loss rates of $\sim40\%$~Gyr$^{-1}$. These catalogues will be made publicly available.

22 pages, 20 figures, accepted for publication in MNRAS