Axioms of Hamilton theories of general type including classical and quantum ones as particular cases

The set of Axoims of the Hamiltonian theory is constructed in the form which is valid for classical and quantum theoris as well. These Axioms define the algebra with two multiplication operations called the free Hamiltonian algebra. Classical and quantum theoris are derived as factor algebras corresponding to different equivalence relations. The Axioms admits essentially new Hamiltonian theories with the nonassociative multiplication of the observables