  Magic-angle twisted bilayer graphene (MA-TBG) exhibits intriguing quantum
phase transitions triggered by enhanced electron-electron interactions when its
flat-bands are partially filled. However, the phases themselves and their
connection to the putative non-trivial topology of the flat bands are largely
unexplored. Here we report transport measurements revealing a succession of
doping-induced Lifshitz transitions that are accompanied by van Hove
singularities (VHS) which facilitate the emergence of correlation-induced gaps
and topologically non-trivial sub-bands. In the presence of a magnetic field,
well quantized Hall plateaus at filling of 1, 2, 3 carriers per moir\'e-cell
reveal the sub-band topology and signal the emergence of Chern insulators with
Chern-numbers, ! = !, !, !, respectively. Surprisingly, for magnetic fields
exceeding 5T we observe a VHS at a filling of 3.5, suggesting the possibility
of a fractional Chern insulator. This VHS is accompanied by a crossover from
low-temperature metallic, to high-temperature insulating behavior,
characteristic of entropically driven Pomeranchuk-like transitions,
