  In order to study certain algebraic objects, and notably algebraic groups,
Serre introduced the notion on invariants, in particular cohomological
invariants. The construction of non-trivial cohomological invariants of
algebraic groups is an active area of modern research, and very few invariants
are known in degree greater than 3.
  In the first chapter, we give a complete description of Witt and
cohomological invariants of the functors In as combinations of fundamental
invariants behaving like divided powers, whose construction relies crucially on
lambda operations in the Grothendieck-Witt ring. We also study the behaviour of
these invariants with respect to various operations such as products or
similitudes.
  The second chapter is dedicated to the construction of a "mixed" Witt ring
associated to an algebra with involution : the fundamental idea is to define
the product of two $\epsilon$-hermitian forms using a Morita equivalence given
by the involution trace form of the algebra. We also define lambda operations
on the mixed Grothendieck-Witt ring, as well as a fundamental filtration
imitating the split case. A particular attention is given to explicit
calculations in the case of algebras of index 2.
  We use those tools in the third chapter to mimic the constructions of chapter
1 in the framework of hermitian forms, and thus construct cohomological
invariants of algebras with involution, with more detailed results in index 2.
The main interest is to be in principle able to define non-trivial invariants
of arbitrarily high degree, although the index constitues a form of
obstruction.
