#### Title of Thesis:

Formality and homotopy automorphisms in rational homotopy theory

#### Author of Thesis:

Bashar Saleh

#### External reviewer:

Marco Manetti (Sapienza Università di Roma)

#### Supervisor:

Alexander Berglund

#### Abstract:

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 a dg Lie algebra is formal if and only if its universal enveloping algebra is formal. We also prove that a commutative dg algebra is formal as a dg associative algebra if and only if it is formal as a commutative dg algebra. We present some consequences of these 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.