An Invitation to Unbounded Representations of *-Algebras on Hilbert Space

General Notation.- 1 Prologue: The Algebraic Approach to Quantum Theories.- 2 *-Algebras.- 3 O *-Algebras.- 4 *-Representations.- 5 Positive Linear Functionals.- 6 Representations of Tensor Algebras.- 7 Integrable Representations of Commutative *-Algebras.- 8 The Weyl Algebra and the Canonical Commutation Relation.- 9 Integrable Representations of Enveloping Algebras.- 10 Archimedean Quadratic Modules and Positivstellensätze.- 11 The Operator Relation X X *= F ( X * X ).- 12 Induced *-Representations.- 13 Well-behaved *-Representations.- 14 Representations on Rigged Spaces and Hilbert C *-modules. A Unbounded Operators on Hilbert Space.- B C *-Algebras and Representations.- C Locally Convex Spaces and Separation of Convex Sets.- References.- Symbol Index.- Subject Index.