1 Introduction.- 2 Operator Algebras.- 3 Gleason Theorem.- 4 Completeness Criteria.- 5 Generalized Gleason Theorem.- 6 Basic Principles of Quantum Measure Theory.- 7 Applications of Gleason Theorem.- 8 Orthomorphisms of Projections.- 9 Restrictions and Extensions of States.- 10 Jauch-Piron States.- 11 Independence of Quantum Systems.