I translated the title from Japanese to English. "Matoba Risa-chan" is Risa Matoba-chan, the subject of the phrase. "de" is the means of how we are using the verb, "Manabu", which is studying. "Doubutsu" is animal and "Koubi" is mating. Joined by "no", it becomes the noun phrase animal mating. So we are studying how animal mate using Risa-chan.