A comprehensive theory encompassing the kinetics of the sol-to-gel transition is yet to be formulated due to break-down of the mean-field Smoluchowski Equation. Using high temporal-resolution Monte Carlo simulation of irreversible aggregation systems, we show that this transition has three distinct regimes with kinetic exponent z is an element of [1.2) corresponding to aggregation of sol clusters proceeding to the ideal gel point (IGP); z is an element of [2,5.7) for gelation of sol clusters beyond IGP; and z is an element of [2,3.5) for a hitherto unidentified regime involving aggregation of gels when monomer-dense. We further establish universal power-law scaling relationships that connect the kinetics of these three regimes. Improved parameterizations are performed on the characteristic timescale parameters that define each regime. (C) 2019 Elsevier Inc. All rights reserved.