We report a high-statistics measurement of the differential cross section of the process γγ → K0SK0 S in the range 1.05 GeV ≤ W ≤ 4.00 GeV, where W is the center-of-mass energy of the colliding photons, using 972 fb-1 of data collected with the Belle detector at the KEKB asymmetric-energy e +e- collider operated at and near the ρ-resonance region. The differential cross section is fitted by parameterized S-, D 0-, D2-, G0-, and G2-wave amplitudes. In the D2 wave, the f2(1270), a 2(1320), and f2′(1525) are dominant and a resonance, the f2(2200), is also present. The f0(1710) and possibly the f0(2500) are seen in the S wave. The mass, total width, and product of the two-photon partial decay width and decay branching fraction to the K K̄ state ΓγγΒ(K K̄) are extracted for the f2′(1525), f 0(1710), f2(2200), and f0(2500). The destructive interference between the f2(1270) and a2(1320) is confirmed by measuring their relative phase. The parameters of the charmonium states Χc0 and Χc2 are updated. Possible contributions from the Χc0(2P) and Χ c2(2P) states are discussed. A new upper limit for the branching fraction of the P- and CP-violating decay channel ηc → K0SK0S is reported. The detailed behavior of the cross section is updated and compared with QCD-based calculations.