  Our experience shows that dealing with noncommutative objects one should not
imitate the classical commutative mathematics, but follow "the way it is"
starting with basics. In this paper we consider mainly two such problems:
noncommutative Pl\"ucker coordinates (as a background of a noncommutative
geometry) and noncommutative Bezout and Vieta theorems (as a background of
noncommutative algebra). We apply these results to the theory of noncommutative
symmetric functions started by Gelfand, Krob, Lascoux, Leclerc, Retakh, Thibon.
We also continue our investigation of noncommutative continued fractions and
almost triangular matrices. It turns out that this problem is related with a
computation of quantum cohomology.
