  In this paper we use a constructive approach based on gauge invariant
description of massive high spin particles for investigation of possible
interactions of massive spin 2 particle. We work with general case of massive
spin 2 particle living in constant curvature $(A)dS_d$ background, which allows
us carefully consider all flat space, massless or partially massless limits. In
the linear approximation (cubic terms with no more than two derivatives in the
Lagrangians and linear terms with no more than one derivative in gauge
transformations) we investigate possible self-interaction, interaction with
matter (i.e. spin 0, 1 and 1/2 particles) and interaction with gravity.
