Hermitian K-theory -------------------- This subject is related to the classication of Hermitian forms over a ring with involution (Witt groups) and to higher algebraic K-theory. After stating the basic definitions, the aim of the lecture is to study two main themes : 1) The analog of Bott periodicity in the context of Hermitian forms. In fact our main theorem implies classical Bott periodicity in Topology. 2) We prove that this analog of Bott periodicity implies a calculation of the Hermitian K-theory of the integers (this is joint work with J. Berrick). ------------------------------