The problem of Petri nets application to real-world parallel and distributed systems of industrial size causes developing of the compositionality within the theory of Petri nets. This paper presents a tool which is an attempt to resolve this problem. We suggest a solution based on an algebraic approach, of Petri net representation. Two levels of compositionality are introduced. The first one, algebraic level offers to a designer a set of net operations (sequential, alternative and parallel composition, iteration and disruption), which allow to build complex Petri nets from simpler ones. The second architectural level allows the user to manipulate with Petri net entities, where the entity is defined to be a Petri net equipped with access points. The suggested technique is implemented in a three-level Petri net editor comprising basic, algebraic and architectural editors.