Let V be a finite classical polar space of finite dimension, f (resp. Q) its associated polarity (quadratic form), \({\mathcal O}\) an ovoid in V (i.e. a set of singular points such that every maximal totally singular subspace meets \({\mathcal O}\) in just one point). \(\Gamma\) denotes the subgroup of those semilinear mappings which preserve the symplectic or unitary polarity f or the quadratic form Q. Two ovoids are called isomorphic iff there exists some element of \(\Gamma\) mapping one onto the other. \(\Gamma_{\{{\mathcal O}\}}\) and \(\Gamma_{({\mathcal O})}\) denote the setwise and pointwise stabilizer of \({\mathcal O}\) in \(\Gamma\), respectively, Aut(\({\mathcal O}):=\Gamma_{\{{\mathcal O}\}}/\Gamma_{({\mathcal O})}.\)
In his main theorem the author gives a classification (up to isomorphism) of ovoids \({\mathcal O}\), if Aut(\({\mathcal O})\) acts two-transitively on the points of \({\mathcal O}\). This classification is carried out in terms of Aut(\({\mathcal O})\) and the group G of isometries of V. With only one exception he finds unique isomorphism classes. All the ovoids occurring in the classification have already been described elsewhere, cf. J. W. P. Hirschfeld [Finite projective spaces of three dimensions (1985; Zbl 0574.51001); p. 46ff], W. M. Kantor [Can. J. Math. 34, 1195- 1207 (1982; Zbl 0467.51004)], and J. A. Thas [Geom. Dedicata 10, 135-143 (1981; Zbl 0458.51010)]. The proof uses the classification of the finite 2-transitive permutation groups.