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Reverse engineering software systems has become a major concern in software industry because of their sheer size and complexity. This problem needs to be tackled since the systems in question are of considerable worth to their owners and maintainers. In this article, we present the concept of a polymetric view, a lightweight software visualization technique enriched with software metrics information. Polymetric views help to understand the structure and detect problems of a software system in the initial phases of a reverse engineering process. We discuss the benefits and limits of several predefined polymetric views we have implemented in our tool CodeCrawler. Moreover, based on clusters of different polymetric views, we have developed a methodology which supports and guides a software engineer in the first phases of a reverse engineering of a large software system. We have refined this methodology by repeatedly applying it on industrial systems and illustrate it by applying a selection of polymetric views to a case study.