Table of Contents1. Axiomatic Formalism.- 1.1. Introduction. The Algebraic Approach as a Local Quantum Theory.- 1.2. Axioms of the Algebraic Approach.- 1.3. Structure of the Local Quantum Theory: Theorems Derived from the Axioms.- 2. From the Theory of Observables to the Theory of Quantum Fields.- 2.1. Global Theory of Superselection Rules.- 2.2. Local Theory of Superselection Rules: Equivalence Properties of Coherent Sectors.- 2.3. Program for Producing Field Theory by Means of Reconstructing its Charge Sectors.- 3. Field Algebras and their Applications.- 3.1. Op*-Algebras of Field Operators and Vacuum Superselection Rules.- 3.2. Construction and Properties of Von Neumann Field Algebras.- 3.3. Free and Generalized Free Fields.- Appendix. Problems of Constructing Algebraic Gauge Quantum Field Theory.- References.