  This habilitation memoir (in French, submitted in May 2014) is made up of
five chapters, each being an introduction to work of the author between 2006
and 2014. The core of the memoir consists of the first three chapters,
pertaining to geometric group theory. More precisely, it is concerned with
large-scale geometry of groups and especially Lie groups (Chapters 1 and 2),
and locally compact hyperbolic groups (Chapter 3). Chapter 4 is concerned with
the study of groups through their unitary representations and their isometric
actions on Hilbert spaces (Kazhdan and Haagerup properties). Finally, Chapter 5
is more concerned with "structural" group theory, studying, for a given group
(discrete, or more generally locally compact), the space of its closed
subgroups, or closed normal subgroups. A list of open questions is appended.
While the memoir mostly surveys published papers, it also presents some
unpublished corollaries in Chapter 1 about asymptotic cones of Lie groups.
