The critical analysis of the generally accepted foundations of theory of photon (quantum) gas are proposed. The principle of the unity of formal logic and of rational dialectics is the correct methodological basis of the analysis. The new results – the correct quantum-statistical foundations – obtained within the framework of the formulated master equation taking into consideration both the quantum states of the radiating molecule and the quantum states of the photon gas in the isolated macroscopic systems “molecule + molecular gas + monochromatic photon gas” are as follows: (a) Planck’s, Einstein’s, and Bose’s works on the theory of photon (quantum) gas contain logical errors; (b) photon (quantum) gas being born by radiating molecule obeys “Gibbs statistics”: equilibrium photon (quantum) gas is described by Gibbs quantum canonical distribution; (c) Planck function (“Bose’s distribution”) is an consequence of Gibbs quantum canonical distribution; (d) Einstein coefficients (i.e. the coefficients of spontaneous emission, induced emission and absorption) are equal to each other.