  A general quasi-phenomenological theory that describes phases and phase
transitions of ferromagnetic superconductors with spin-triplet electron Cooper
pairing is presented. The theory is based on extended Ginzburg-Landau expansion
in powers of superconducting and ferromagnetic order parameters. A simple form
for the dependence of theory parameters on the pressure ensures a correct
theoretical outline of the temperature-pressure phase diagram where a stable
phase of coexistence of p-wave superconductivity and itinerant ferromagnetism
appears. This new theory is in an excellent agreement with the experimental
data for intermetallic compounds, for example, UGe2, URhGe, UCoGe, and UIr that
are experimentally proven to be itinerant ferromagnets exhibiting spin-triplet
superconductivity. The mechanism of appearance of superconductivity due to
itinerant ferromagnetism ($M$-trigger effect) is established and demonstrated.
On the basis of the same theory, basic features of quantum phase transitions in
this type of ferromagnetic superconductors are explained in agreement with the
experimental data. The theory allows for a classification of the spin-triplet
ferromagnetic superconductors in two different types: type I and type II. The
classification is based on quantitative criteria, i.e., on simple relations
between theory parameters. Both theory and experiment indicate that the two
types of p-wave ferromagnetic superconductors are well distinguished by
essential differences in their physical properties.
