  We develop the details of Kontsevich's proof of the formality of little
N-disks operad over the field of real numbers. Formality holds in the category
of operads of chain complexes and also in some sense in the category of
commutative differential graded algebras, which is the category encoding "real"
homotopy theory. We also prove a relative version of the formality for the
inclusion of the little m-disks operad in the little N-disks operad for
N>=2m+1.
