Experimental and theoretical results on recording of spatial gratings with interfering femtosecond pulses at $388\mathrm{nm}$ and time-resolved Bragg-matched readout at $776\mathrm{nm}$ are presented for $\mathrm{Li}\mathrm{Nb}{\mathrm{O}}_3$ crystals. These include dependences of the diffraction intensity on the time delay between probe and pump pulses, on the pump intensity and angle, and on the crystal composition. The grating buildup involves instantaneous and quasi-permanent changes of the refractive index and the absorption coefficient. These changes are due to Kerr and two-photon absorption effects and the modulation of photoexcited carriers, respectively. A good agreement between theory and experiment is achieved. Our analysis provides an understanding of nonlinear optical phenomena in $\mathrm{Li}\mathrm{Nb}{\mathrm{O}}_3$ crystals on the femtosecond time scale. The theory is applicable to a large range of optical materials with modestly wide, $\approx 3\text{to}5\mathrm{eV}$ , bandgap.