  A mathematically rigorous relativistic quantum Yang-Mills theory with an
arbitrary semisimple compact gauge Lie group is set up in the Hamiltonian
canonical formalism. The theory is non-perturbative, without cut-offs, and
agrees with the causality and stability principles. This paper presents a fully
revised, simplified, and corrected version of the corresponding material in the
previous papers DYNIN[11] and [12]. The principal result is established anew:
due to the quartic self-interaction term in the Yang-Mills Lagrangian along
with the semisimplicity of the gauge group, the quantum Yang-Mills energy
spectrum has a positive mass gap. Furthermore, the quantum Yang-Mills
Hamiltonian has a countable orthogonal eigenbasis in a Fock space, so that the
quantum Yang-Mills spectrum is point and countable. In addition a fine
structure of the spectrum is elucidated.
  KEYS: Millennium Yang-Mills problem; Finite propagation speed; Sobolev
inequalities; Nuclear vector spaces; Infinite-dimensional holomorphy;
Friedrichs operator extensions; Variational spectral principle; Symbols and
spectral theory of pseudo-differential operators.
