A topological crystalline insulating (TCI) state has recently been identified in Pb1-xSnxTe. This unique state of topological matter allows the presence of an even number of Dirac surface states at mirror symmetric points in the Brillouin zone, where a band inversion occurs. The band inversion can be induced and controlled in Pb1-xSnxTe by increasing x beyond a critical value, or by cooling down past a critical temperature at fixed x. Pb1-xSnxTe is thus an ideal test-bed to study the physics of this band inversion – also referred to as the topological phase transition. We combine high field Shubnikov-de-Haas oscillations measurements (up to B=60T) and infrared magnetooptical Landau level spectroscopy to probe the Fermi surface of Pb1-xSnxTe as a function of x and temperature. We are able to comprehensively map out the full band structure using these two techniques. We first establish a topological phase diagram of the bulk states in Pb1-xSnxTe for 0≤x≤0.6, based on the variation of the band gap, its inversion and the observation of topological surface states either in cyclotron resonance or Shubnikov-de-Haas measurements. We also study in detail the quantum oscillations pertaining to surface states for x=0.46 as a function of temperature. This allows us to trace the continuous variation of the Berry phase through the topological phase transition as temperature is increased past the critical temperature where the band inversion occurs. Our results pave the way for a deeper fundamental understanding of the nature of the band inversion in IV-VI semiconductors, and other similar systems.