This book presents an in-depth study of the families of

Galois representations carried by the p -adic eigenvarieties

attached to unitary groups. The study encompasses some

general algebraic aspects (properties of the space of representations

of a group in the neighbourhood of a point, reducibility

loci, pseudocharacters), and other aspects more

specific to Galois groups of local or number fields. In particular,

we define and study certain deformation functors

of crystalline representations of the absolute Galois group

of Q_p, namely trianguline deformations , which are naturally

associated to the families above. As an application, we show

how the geometry of these eigenvarieties at "classical" points

is related to the dimension of certain Selmer groups. This,

combined with conjectures of Langlands and Arthur on the

discrete automorphic spectrum of unitary groups, allows us

to prove, amongst other things, new cases of the Bloch-Kato

conjectures (in any dimension).