It is shown by the method of 2-dinıensional cross-section that for the class S of a- nalytic and schlicht functions the inequaiity /(z) = z + l-l< L a. İS always true, with equality for any n, n 2 if and only if/(s) is a Koebe func- tion. Survey. In this paper we prove the fam o us Bieberbach’s conjecture, i. e., for the class S of analytic and schlicht functions f(z) ~ z a2Z^ + a,z^ + 1, the inequality i «n I n I 2 I is ahvays true, with equality for any n, n is a Koebe function ’ 2, if and only (1—<>i't2)‘ = 2 + 2ei9 2^ -|- 3e2i6 z’ •••5 9 real- Up to now, the conjecture has only been proved for re = 2, 3, 4 (see: [2], [3], [4], [5]). As usual let V,n-1 be the set of pOints a = ^^3, ®n-ı) belonging to functions