The family of geometric axioms generalizing Veblen, Tamaschke and Desargues axioms for geometric spaces is introduced and relations among them are studied. Geometric space is defined as a point set X together with a parallelism \(: X^ 2\to R\) (R is the set of directions). Special cases, namely group fiberings are described in more details. Finally the solution of the main problem in noncommutative geometry (which was introduced by J. André), namely to give a geometric description of a geometric space to be the group space for a direct product of finite geometric spaces and for groups fiberings, are presented.