This project will develop and test a mathematical theory that describes the interaction between attention and memory in the acquisition of automatic skills and in the expression of those skills in performance. The theory combines in a common formal structure two theories developed by the Principal Investigator with previous NSF support. One is a theory of attention that describes how stimuli are selected and how responses to those stimuli are generated. The other is a theory of memory that describes how a domain-specific knowledge base builds up over extensive practice on the task. The proposed research consists of three empirical projects that test the theory's assumptions about learning, representation, and real-time processing, and a theoretical project that extends the theory and relates it to formal theories of memory and cognitive control. The basic idea behind the theory is that attention governs access to memory, determining what is learned from experience and what is retrieved from memory to support performance on various tasks. Memory records the things that attention selects, and the things that attention selects act as retrieval cues, pulling from memory information relevant to the task at hand. Memory also governs attention, determining the set of alternatives that attention chooses among. To attend is to interpret and categorize, and memory provides the categories. The theory suggests that this interaction between memory and attention is ubiquitous, occurring in every act of cognition. Thus, the theory is broad in scope. Its formal structure and formal relations to other theories give it depth as well as breadth. It allows analytical, quantitative predictions of the interaction between attention and memory. The proposed research is significant theoretically and practically. From a theoretical perspective, it integrates research on attention and memory, revealing quantitative and qualitative relations between phenomena that were previously regarded as separate. It takes important steps toward a unified theory of cognition, providing a coherent account of many important phenomena in a common formal structure. From a practical perspective, the theory and the experiments conducted to test it will have strong implications for training and education, providing a principled way to design training programs that maximize generalization (e.g., from the classroom to the workplace) and optimize skilled performance. `There is nothing so practical as a good theory.`