In this paper we introduce noncommutative fields and forms on a new kind of noncommutative algebras: -algebras. We also define the Frõlicher-Nijenhuis bracket in the noncommutative geometry on rho-algebras.

In this paper we present a new aproach of the noncommutative geometry of the matrix algebra M_{n}(C). We define two different differential calculi, and we introduce linear connections on M_{n}(C), using the framewok of rho-algebras

In this paper we introduce the basic notions from noncommutative geometry to the quantum hyperplane: linear connections, submanifolds, distributions and we give a Frobenius type theorem for the quantum hyperplane.

In this paper we study linear connection on bimodules over almost commutative algebras using the framework of noncommutative geometry. We also present its curvature and its torsion. As an example there are presented linear connections on N-dimmensional quantum hyperplane over two kind of bimodules.