This is a continuation of the talk from last week about the regularizing properties of free additive convolution. We introduce and discuss a variety of tools from noncommutative probability, notably the operations of free, boolean, and monotone additive and multiplicative convolutions, the Belinschi–Nica semigroup, the free divisibility indicator, and complex subordination. The goal of the talk is to provide a broad overview of free probability, including a variety of curious equations and identities, from a complex analytic viewpoint. The talk is based on the works of Belinschi, Bercovici, Nica, Arizmendi, and Hasebe.