In this thesis, we give new examples and constructions for infinite-dimensional Lie groups. At the beginning, we construct a smooth Lie group structure on the group of real analytic diffeomorphisms of a compact real analytic manifold with corners. In the following part, we examine conditions for the integrability of a given Banach subalgebra of the Lie algebra of a Lie group that is modelled on a locally convex space. For that reason, we elaborate a corresponding Frobenius theorem. In the third part of this thesis, we show that the canonical invariant symmetric bilinear form on the Lie algebra of compactly supported sections of a finite-dimensional perfect Lie algebra bundle is universal in a topological sense. At the end of this thesis, we construct central extensions of Lie groups of compactly supported sections of Lie group bundles over non-compact base manifolds. In addition we show the universality of certain examples of these central extensions.