This book offers a unique, comprehensive, technically in-depth, and up-to-date treatment of modeling economic agreements by applying recent results of advanced algebras, representation theory, theory of categories, and transmutation theory. The importance of a new concept of agreements, as introduced here, is derived from a general impossibility of making a complete contract for any nontrivial economic transaction. The proposed extensions provide foundations rich enough to follow the complexity of economic property rights, including entrepreneurial agreements, clubs and transfers through the restructuring processes. The book is relevant for academics with a theoretical interest in economics, applied mathematics, mathematical economics, operational research and advance management of tangible and intangible assets. It provides full details and line-by-line proofs of all basic relations needed for research in modeling issues of economic property rights theory and economic agreements.