Newton's Laws of Classical Mechanics are valid in which frames of reference?

An inertial frame of reference is that frame for which the so-called law of inertia is fulfilled, also known as First Law of Classical Mechanics of Isaac Newton (January 4, 1642 - March 31, 1727), which states that a body tends to maintain its state of rest or of rectilinear and uniform movement if it does not interact with any other body or if the interactions on it are compensated. Similarly, it is then defined that a non-inertial frame of reference is one where, in the absence of interactions or with its interactions compensated, a body does not remain at rest nor maintain a state of rectilinear and uniform motion. The 2nd and the 3rd Newton's Laws of Classical Mechanics also are fulfilled only in inertial frames of reference.

This seemingly 'simple' principle, already discovered before by Galileo Galilei (February 15, 1564 - January 8, 1642), sometimes called Galileo's Relativity Principle, constitutes, in some way, the basis of all the Physics that came after Isaac Newton, including Thermodynamics and Gas Theory, Classical Electrodynamics, Special and General Theory of Relativity, and the Quantum Mechanics, to this day.

A curiosity: Newton was born 4 days after Galileo's death (January 8 and 4, 1642). It was as if Divine Providence did not want the world to be orphaned of a mind of such greatness for a long time!