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Software design is on its way from craft to craftsmanship to engineering. Craft is based on empirical methods and craftsmanship is a higher level of craft. However, empirical methods rarely work for very complex systems. Thus, now when software development and software services have become an industry, it is necessary to make a transition from craft to engineering. Engineering, in general, is defined as application of scientific principles to practical ends, as the design, manufacture, and operation of structures and mechanisms. Computer programs have extremely sophisticated structures. Consequently, it is necessary to provide scientific principles and technologies based on these principles for the design, manufacture, and operation of these structures. This is the main task of computer science. A perspective source of technological tools for software engineering is the mathematical schema theory. Its structures and methods allow one to develop efficient working technology for software engineering. Schemas in the form of flow-charts have been used as organizational units from the very beginning of computer technology development and utilization. However, they have been empirically used without appropriate theoretical support. Now the Unified Modeling Language (UML) is the industry-standard language for specifying, visualizing, constructing, and documenting the artifacts of software systems in a form of UML diagrams, which are also informal schemas. UML simplifies the complex process of software design, making a "blueprint" for construction, but only on the level of software architecture and without sufficient formalization to allow application of mathematics to software design. Formalizations of schemas constructed earlier, such as program schemata or schemes in logic, have too many restrictions or are too abstract for application in software industry. The new level of the scientific discipline that studies schemas, the mathematical schema theory, extends applicability of computer science and mathematics to software engineering, providing software engineers with basic tools for the software design, manufacture, and operation.