  The time-convolutionless master equation provides a general framework to
model non-Markovian dynamics of an open quantum system with a time-local
generator. A diagrammatic representation is developed and proven for the
perturbative expansion of the exact time-local generator for an open quantum
system interacting with arbitrary environments. A truncation of the
perturbation expansion leads to the perturbative time-convolutionless quantum
master equations. We further introduce a nonperturbative approach that
approximates the time-convolutionless generator as a nested time-ordered
exponential function.
