  We report our survey of $\gamma$\,Doradus stars from the 4-yr \textit{Kepler}
mission. These stars pulsate mainly in g modes and r modes, showing
period-spacing patterns in the amplitude spectra. The period-spacing patterns
are sensitive to the chemical composition gradients and the near-core rotation,
hence they are essential for understanding the stellar interior. We identified
period-spacing patterns in 611 $\gamma$\,Dor stars. Almost every star pulsates
in dipole g modes, while about 30\% of stars also show clear patterns for
quadrupole g modes and 16\% of stars present r mode patterns. We measure
periods, period spacings, and the gradient of the period spacings. These three
observables guide the mode identifications and can be used to estimate the
near-core rotation rate. We find many stars are hotter and show longer
period-spacing patterns than theory. Using the Traditional Approximation of
Rotation (TAR), we inferred the asymptotic spacings, the near-core rotation
rates, and the radial orders of the g and r modes. Most stars have a near-core
rotation rate around $1$\,$\mathrm{c/d}$ and an asymptotic spacing around
4000\,s. We also find that many stars rotate more slowly than predicted by
theory for unclear reasons. 11 stars show rotational splittings with fast
rotation rates. We compared the observed slope--rotation relation with the
theory and find a large spread. We detected rotational modulations in 58 stars
and used them to derive the core-to-surface rotation ratios. The interiors
rotate faster than the cores in most stars, but by no more than 5\%.
