Despite that in nowadays exists a bunch of software modeling languages (including the Unified Modeling Language (UML)) and methods that consumes such modeling languages, the way software is built remains surprisingly primitive (by meaning that major software applications are cancelled, overrun their budgets and schedules, and often have hazardously bad quality levels when released). This phenomenon can be explained by the fact that the problem domain exists separately from the solution domain (i.e., by not paying appropriate attention to the analysis of the problem domain functioning). Furthermore, in particular cases the software is built as the developers see the solution and not as the problem domain functions. By reducing or even avoiding proper analysis of the problem domain, the traces between problem and solution domain cannot be established. Without traces between both domains the acceptance process of developed software gets meaningless since the customer cannot fully verify the delivered solution (in terms of relating problem domain to the software). The main purpose of this doctoral thesis titled “Topological Unified Modeling Language: Development and Application” is researching UML and software development methods that support and promote the application of UML. The aim of the research is to create a new version of UML that can be applied in a formal way which allows clearly tracing cause-and-effect relationships between the problem and solution domains. To achieve the goal of this thesis a new language is developed – Topological Unified Modeling Language (TopUML) – and its supporting software development method – TopUML modeling. The TopUML includes elements that allow formally relating problem and solution domains while the TopUML modeling promotes formal software development process. In short – TopUML modeling ensures that software artifacts are created in a strong conformance with the functioning of the problem domain. The developed language and TopUML modeling method are applied in an experimental project and in a case study project. The experimental project includes software designing for laundry problem domain at the computation and platform independent viewpoints, while during the case study project enterprise data synchronization software is designed and developed which currently operates in production environment.