In the past 40 years the user interface of computers evolved from a text-based terminal environment to a complex, realistic and more helpful form to make the control of the processes and communication easier. In my thesis I first summarize the important stations of this evolution and mention new incipient ways of computer UI. This is followed by the description of the techniques needed to create modern UIs on OSX and iOS platforms, where I also investigate the differences of the two environments. Then I specify the first part of my thesis, the animation library and give a theoretical introduction about the more important concepts and techniques. The next chapter is about the demonstration of the library by its components. After the library I detail the planning of the presentation application. This plan contains the definition of the use cases, interfaces, necessary techniques and tools. As closure I describe the components of the application and their connection. The next to last chapter is about the implementation of the animation library and the presentation application. In the end of my thesis I list those features that are out of its short scope.