Group schemes over a field -- Group subschemes of a group scheme -- Coalgebras over a field -- Hopf algebras over a field -- Structures of colocal bigebras -- Formal groups over a field -- Structures of formal groups as local rings -- Algebraic Hopf subalgebras -- Rational representations of group schemes -- Joins and intersections of group subschemes -- Adjoint representations of group schemes -- Normalizers of Hopf subalgebras and group subschemes -- Centralizers of Hopf subalgebras and group subschemes -- Commutators of Hopf subalgebras and group subschemes -- Lie algebras attached to group schemes -- Left invariant semi-derivations of group varieties -- Algebraic schemes on which a group scheme operates -- Isogenies of group varieties -- Kernels of purely inseparable isogenies