This innovative text focuses on the architectures, mathematics, and algorithms that are integral to creating reliable user interfaces. The first sixteen chapters cover the concepts required for current graphical user interfaces, including specific emphasis on the Model-View-Controller architecture. The second part of the book provides an overview of key research areas in interactive systems, with a focus on the algorithms required to implement these systems. Using clear descriptions, equations,and pseudocode, this text simplifies and demystifies the development and application of a variety of user interfaces.