Experimental data for the paper "Nonlinear THz Control of the Lead Halide Perovskite Lattice", published with open-access in Science Advances under https://doi.org/10.1126/sciadv.adg3856 The data was measured at the Department of Physical Chemistry, Fritz Haber Institute of the Max Planck Society in Berlin. Contents: THz E-field data from Fig. 1 THz-induced Kerr effect time domain data, fluence dependence, azimuthal angle dependence, and corresponding THz fields for MAPbBr3 and CsPbBr3 at room temperature from Fig. 2. THz-induced Kerr effect time domain data for MAPbBr3 single crystals and thin films for room temperature, 180K and 80K from Fig. 3. THz-induced Kerr effect experimental data and simulated Kerr signals from Fig. 4. THz-induced Kerr effect time domain data for MAPbBr3 single crystal at different THz fluences from Fig. 5a. Raw data and data of the Supplementary Materials (SM) will be provided upon request. Please contact Maximilian Frenzel (frenzel@fhi-berlin.mpg.de) and Sebastian F. Maehrlein (maehrlein@fhi-berlin.mpg.de) for such a request or for general questions.

S.F.M. acknowledges funding for his Emmy Noether group from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation, Nr. 469405347). S.F.M and L.P acknowledge support of the 2D-HYPE project from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation, Nr. 490867834) and Agence Nationale de la Recherche (ANR, Nr. ANR-21-CE30-0059), respectively. XYZ acknowledges support by the Vannevar Bush Faculty Fellowship through Office of Naval Research Grant # N00014-18-1-2080. M.C. was supported by the DAAD Scholarship 57507869.