  We define motivic iterated integrals on the affine line, and give a simple
proof of the formula for the coproduct in the Hopf algebra of they make. We
show that it encodes the group law in the automorphism group of certain
non-commutative variety. We relate the coproduct with the coproduct in the Hopf
algebra of decorated rooted planar trivalent trees - a planar decorated version
of the Hopf algebra defined by Connes and Kreimer. As an application we derive
explicit formulas for the coproduct in the motivic multiple polylogarithm Hopf
algebra. We give a criteria for a motivic iterated integral to be unramified at
a prime ideal, and use it to estimate from above the space spanned by the
values of iterated integrals. In chapter 7 we discuss some general principles
relating Feynman integrals and mixed motives.
