  The review of modern study of algebraic, geometric and differential
properties of quaternionic (Q) numbers with their applications. Traditional and
"tensor" formulation of Q-units with their possible representations are
discussed and groups of Q-units transformations leaving Q-multiplication rule
form-invariant are determined. A series of mathematical and physical
applications is offered, among them use of Q-triads as a moveable frame,
analysis of Q-spaces families, Q-formulation of Newtonian mechanics in
arbitrary rotating frames, and realization of a Q-Relativity model comprising
all effects of Special Relativity and admitting description of kinematics of
non-inertial motion. A list of "Quaternionic Coincidences" is presented
revealing surprising interconnection between basic relations of some physical
theories and Q-numbers mathematics.
