retained austenite

There is no "formation" of retained austenite. It's a result of quenching.

Quenching heat treatment is accomplished by heating the steel to a temperature high enough to allow the complete mass be in the austenitic form and then a quick cooling (water, oil and even air cooling). The quenching purpose use to be to transform by this fast cooling the austenite in a no-equilibrium phase, usually martensite which is much harder (and more fragile).

Cooling up to room temperature, sometimes doesn't give time enough to achieve complete transformation of austenite to martensite, and as a result, some austenite is still present even theoretically austenite isn't stable at room temperature ( in fact for plain carbon steel is stable only above 723ºC).

During quenching, there is a temperature at which austenite begins to transform to martensite. It's called M_s. And the temperature when the transformation has finished is called M_f. In many steels M_f temperature is below room temperature, so full transformation of austenite cannot occur by simple quenching.

That amount of austenite not transformed during quenching is what is called "retained austenite".

If after quenching a tempering treatment is given, some or all of the "retained austenite" transforms into more stable phases.

Sometimes, when M_f is below room temperature and full transformation (no retained austenite) is desired, there is a sort of quench called "sub-zero quenching" in which the quenching bath is at much lower than room temperatures, at least to reach M_f.

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