While neuroscientists garner success in identifying brain regions and in analyzing individual neurons, ground is still being broken at the intermediate scale of understanding how neurons combine to encode information. This book proposes a method of representing information in a computer that would be suited for modeling the brain's methods of processing information. Holographic Reduced Representations (HRRs) are introduced here to model how the brain distributes each piece of information among thousands of neurons. It had been previously thought that the grammatical structure of a language cannot be encoded practically in a distributed representation, but HRRs can overcome the problems of earlier proposals. Thus this work has implications for psychology, neuroscience, linguistics, and computer science, and engineering.