This book describes the construction of algebraic models which represent the operations of the double entry accounting system. It gives a novel, comprehensive, proof based treatment of the topic, using such concepts from abstract algebra as automata, digraphs, monoids and quotient structures. Contents:Approaches to Accounting TheoryTwo Balance VectorsTransactionsAbstract Accounting SystemsQuotient Systems and HomomorphismsAccounting Systems and AutomataAccounting Systems with Restricted TransactionsAlgorithmsThe Extended ModelThe Model IllustratedReadership: Academic economists, accountants, algebraists and applied mathematicians.