Morita's cycles are an infinite sequence of cycles in the unstable (rational) homology of $Out(F_n)$. Their construction is motivated by a remarkable theorem of Kontsevich which relates these homology groups with the cohomology of a certain Lie algebra $\mathfrak{h}_\infty$ associated to the Lie operad.

I will define operads, giving plenty of examples, and introduce the unstable range of $H_\ast(Out(F_n))$, showing where these Morita cycles fit in. I'll then state Kontsevich's theorem and explain how Mortia's observation leads to cycles in the rational homology of $Out(F_n)$.