Uniformally bounded families of holomorphic maps and locally uniform convergence -- Topological consequences of the group structure of the set of automorphisms -- The caratheodory distance and completeness properties of the group of automorphisms -- The Lie algebra of complete vector fields -- The natural topology on the Lie algebra of complete vector fields -- The Banach Lie group structure of the set of automorphisms -- Bounded circular domains -- Automorphisms of the unit ball of some classical Banach spaces -- Bounded symmetric domains -- The Jordan theory of bounded symmetric domains.