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We present a detailed two-dimensional stellar dynamical analysis of a sampleof 44 cosmological hydrodynamical simulations of individual central galaxiesand their satellites. Kinematic maps of the stellar line-of-sight velocity,velocity dispersion, and higher-order Gauss-Hermite moments $h_3$ and $h_4$ areconstructed for each central galaxy and for the most massive satellites. Theamount of rotation is quantified using the $\lambda_{\mathrm{R}}$-parameter.The velocity, velocity dispersion, $h_3$, and $h_4$ fields of the simulatedgalaxies show a diversity similar to observed kinematic maps of early-typegalaxies in the ATLAS$^{\rm{3D}}$ survey. This includes fast (regular), slow,and misaligned rotation, hot spheroids with embedded cold disk components aswell as galaxies with counter-rotating cores or central depressions in thevelocity dispersion. We link the present day kinematic properties to theindividual cosmological formation histories of the galaxies. In general, majorgalaxy mergers have a significant influence on the rotation propertiesresulting in both a spin-down as well as a spin-up of the merger remnant. Lowermass galaxies with significant in-situ formation of stars, or with additionalgas-rich major mergers - resulting in a spin-up - in their formation history,form elongated fast rotators with a clear anti-correlation of $h_3$ and$v/\sigma$. An additional formation path for fast rotators includes gas poormajor mergers leading to a spin-up of the remnants. This formation path doesnot result in anti-correlated $h_3$ and $v/\sigma$. The galaxies mostconsistent with the rare class of non-rotating round early-type galaxies growby gas-poor minor mergers alone. In general, more massive galaxies have lessin-situ star formation since $z \sim 2$, rotate slower and have older stellarpopulations. (shortened)

The ATLAS$^{\rm{3D}}$ project - XXV: Two-dimensional kinematic analysis of simulated galaxies and the cosmological origin of fast and slow rotators