The methods discussed in this work show that the types of changes which may be observed, by precise XAS measurements of Absorbance A versus temperature, across a phase transition are: the changes in the relaxation time of the final states  due to fluctuations near a phase transition; the detection of the anomalous Bragg condition coupled to phonon modes XAS enhancement that identifies the temperature interval where the phonon modes are active, the symmetry changes which introduce new allowed transitions to finite states below an element edge, near Tc indicate what symmetry changes occur, and the method of XTDAFST0 = XAFS(T) - XAFS(T0), allows the precise measurement of the progressive changes in the Debye-Waller factor versus T near a phase transition, and identify (when no other structural changes occur, except in the vibrational modes of a specific bond) the bond responsible for the transition. The methods have been applied to the superconducting transition in layer cuprates and the metal to insulator transition in NiS2-xSex.