  Independent Set Reconfiguration is one of the most well-studied problems in
the setting of combinatorial reconfiguration. It is known that the problem is
PSPACE-complete even for graphs of bounded bandwidth. This fact rules out the
tractability of parameterizations by most well-studied structural parameters as
most of them generalize bandwidth. In this paper, we study the parameterization
by modular-width, which is not comparable with bandwidth. We show that the
problem parameterized by modular-width is fixed-parameter tractable under all
previously studied rules TAR, TJ, and TS. The result under TAR resolves an open
problem posed by Bonsma [WG 2014, JGT 2016].
