The purpose of this thesis is to study the product, the quotients and the suaces of a probabilistic normed space.we study those properties of a PN-space preserved under the operations of formation of product and quotient. Important special cases include the menger probabilistic normed spaces and the serstnev probabilistic normed spaces. These special cases are studied in detail particularly we study conditions under which completeness of a space inheretes to product space, suaces and quotients spaces. we contiue our study by proving a result which shows that a PN-space is a topological group and under certain extra conditions it convents into a topological vector spaces.