Formality and homotopy automorphisms in rational homotopy theory

Sammanfattning: This licentiate thesis consists of two papers treating subjects in rational homotopy theory.In Paper I, we establish two formality conditions in characteristic zero. We prove that adg Lie algebra is formal if and only if its universal enveloping algebra is formal. Wealso prove that a commutative dg algebra is formal as a dg associative algebra if andonly if it is formal as a commutative dg algebra. We present some consequences ofthese theorems in rational homotopy theory.In Paper II, we construct a differential graded Lie model for the universal cover of the classifying space of the grouplike monoid of homotopy automorphisms of a space that fix a subspace.