Book excerpt: In Introduction to the Science of Kinship, Murray J. Leaf and Dwight Read show how humans use specific systems of social ideas to organize their kinship relations and illustrate what this implies for the science of human social organization. Leaf and Read explain that every human society has multiple social organizations, each of which is associated with a distinct vocabulary. This vocabulary is associated with interrelated definitions of social roles and relations. These roles and relations have four specific logical properties: reciprocity, transitivity, boundedness, and imaginary spatial dimensionality. These properties allow individuals to use them in communication to create ongoing, agreed-upon, organizations. This book is recommended for scholars of anthropology, sociology, linguistics, and mathematics.