Adaptive dynamics focuses on assessing the role of natural selection in trait evolution and speciation. I present a new R package, adapt3, that uses matrix projection and individual-based modeling methods to conduct adaptive dynamics analyses. Both pairwise and multiple invasibility analyses are possible, and the resulting population dynamics may be explored to assess evolutionary branching. A series of general projection functions can also yield community projections. I use several key examples to illustrate the use of this package to assess trait evolution and community projection, in particular.