Theo Perator Algebras Associated to Dynamical/Topological/Analytic Objects, and Their Classification Via These Objects, Have Been the Subject of Study By Many Authors For Almost 50 Years, Beginning With the Work of Arveson [4] and Arveson and Josephson [13]. the Main Theme of This Line of Research, As Is the Main Theme of This Paper, Is to Identify the Extent to Which the Dynamical Objects Classify Their Associated Non-Self Operator Algebras. We Shall Mainly Focus on Classification of Non-Self-Adjoint Adjoint Tensor Operator Algebras Arising from a Single C*-Correspondence Over a Commutative C*-Algebra, Although a Profusion of Results Have Been Obtained In Other Contexts to Mention Only Some.