This monograph addresses those interested in the study of planetary or solar magnetic fields, astronomers and geophysicists, researchers and students alike. The authors explore dynamo action under conditions appropriate to large astrophysical bodies, the magnetic Reynolds number of the flow being large compared to unity. In this limit dynamo action becomes closely linked with stretching properties of the flow. The concept of a fast dynamo is explained and studied using various methods from dynamical systems theory. Emphasis is placed on explicit, simple examples of fast dynamos. These examples suggest the beginnings of a theory of fast dynamo action, and link the physical process to the analysis of the stretching, folding, and twisting properties of the flow. A number of special formulations are considered, including dynamo action in almost integrable flows, dynamo action in the anti-integrable limit, and the analysis of random fast dynamos.