Measurements of the polarization and spin correlation in top quark pairs (𝑡 ¯ 𝑡 ) are presented using events with a single electron or muon and jets in the final state. The measurements are based on proton-proton collision data from the LHC at √𝑠 =13 TeV collected by the CMS experiment, corresponding to an integrated luminosity of 138 fb−1. All coefficients of the polarization vectors and the spin correlation matrix are extracted simultaneously by performing a binned likelihood fit to the data. The measurement is performed inclusively and in bins of additional observables, such as the mass of the 𝑡 ¯ 𝑡 system and the top quark scattering angle in the 𝑡 ¯ 𝑡 rest frame. The measured polarization and spin correlation are in agreement with the standard model. From the measured spin correlation, conclusions on the 𝑡 ¯ 𝑡 spin entanglement are drawn by applying the Peres-Horodecki criterion. The standard model predicts entangled spins for 𝑡 ¯ 𝑡 states at the production threshold and at high masses of the 𝑡 ¯ 𝑡 system. Entanglement is observed for the first time in events at high 𝑡 ¯ 𝑡 mass, where a large fraction of the 𝑡 ¯ 𝑡 decays are spacelike separated, with an expected and observed significance of above 5 standard deviations.