This book gives a rigorous, systematic treatment of density estimates, their construction, use and analysis with full proofs. It develops L1 theory, rather than the classical L2, showing how L1 exposes fundamental properties of density estimates masked by L2. The book examines results in simulation, pattern recognition, detection theory, and minimax theory. An extensive bibliography includes references to the recent literature as well as the classical work of Parzen, Rozenblatt and others.