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.