pt. I. Planck's black-body theory, 1894-1906: the classical phase. Planck's route to the black-body problem -- Planck's statistical heritage: Boltzmann on irreversibility -- Planck and the electromagnetic H-theorem, 1897-1899 -- Planck's distribution law and its derivations, 1900-1091 -- The foundations of Planck's radiation theory, 1901-1906 -- pt. II. the emergence of the quantum discontinuity, 1905-1912. -- Dismantling Planck's black-body theory: Ehrenfest, Rayleigh, and Jeans -- A new route to black-body theory: Einstein, 1902-1909 -- Converts to discontinuity, 1905-1910 -- Black-body theory and the state of the quantum, 1911-1912 -- pt. III. Epilogue. Planck's new radiation theory