The book builds theory of motion of charged particles with spin in four-dimensional pseudo-Riemannian space. The theory employs the mathematical apparatus of chronometric invariants by A.L. Zelmanov (physical observable values in the General Theory of Relativity). Numerous special effects in electrodynamics, physics of elementary particles, and cosmology are discussed. The results explain anomalous annihilation of orthopositronium (1987) and link with ``stop of light'' experiment (2001).