  Solar active region (AR) 12673 in 2017 September produced two largest flares
in Solar Cycle 24: the X9.3 flare on September 06 and the X8.2 flare on
September 10. We attempt to investigate the evolutions of the two great flares
and their associated complex magnetic system in detail. Aided by the NLFFF
modeling, we identify a double-decker flux rope configuration above the
polarity inversion line (PIL) in the AR core region. The north ends of these
two flux ropes were rooted in a negative- polarity magnetic patch, which began
to move along the PIL and rotate anticlockwise before the X9.3 flare on
September 06. The strong shearing motion and rotation contributed to the
destabilization of the two magnetic flux ropes, of which the upper one
subsequently erupted upward due to the kink-instability. Then another two sets
of twisted loop bundles beside these ropes were disturbed and successively
erupted within 5 minutes like a chain reaction. Similarly, multiple ejecta
components were detected to consecutively erupt during the X8.2 flare occurring
in the same AR on September 10. We examine the evolution of the AR magnetic
fields from September 03 to 06 and find that five dipoles emerged successively
at the east of the main sunspot. The interactions between these dipoles took
place continuously, accompanied by magnetic flux cancellations and strong
shearing motions. In AR 12673, significant flux emergence and successive
interactions between the different emerging dipoles resulted in a complex
magnetic system, accompanied by the formations of multiple flux ropes and
twisted loop bundles. We propose that the eruptions of a multi-flux-rope system
resulted in the two largest flares in Solar Cycle 24.
