It seems wrong to call desire a theme of Dangerous Liaisons; it would probably be make more sense to call it a driving force, or maybe, the only possible explanation for why anyone would act that way. Desire is not only the motivating force in Dangerous Liaisons, it is itself the most desired commodity. In a society where people live in such luxury that they can want for nothing, the very act of wanting something makes that commodity become valuable.
War, or at least a minor altercation in Corsica, is in the background of Dangerous Liaisons. War is also in the foreground, since battle is the metaphor constantly used by Merteuil and Valmont to describe their amorous exploits.
Religion is another metaphor used to describe love, employed in particular by Valmont. To gain some ground on the Présidente de Tourvel, he writes to her in terms to which she will be forced by her convictions to respond. These are religious terms: for example, Valmont accuses his Présidente of refusing to listen to his prayers, of punishing him unfairly for his misdeeds, and of averting her eyes from him like some unfortunate person one has no intention of assisting. This could be called parody, but Valmont is not mocking, or even imitating, Tourvel's writing style. Rather, he is anticipating her reading style, and how much what she reads will reflect on her. Thus, he invents situations in which she could be responsible for his unhappiness, even though he was the one who started the whole affair. She can only believe what he says if she is sure that it pertains to her. What better way to convince a devout woman, Valmont reasons, than to convince her that she is the one who has done wrong. As the novel progresses, "faith," for the Présidente de Tourvel, has progressively more to do with the duty she owes Valmont than the duty she owes her god.
Education comes in many colors, but in Dangerous Liaisons, "receiving an education" usually refers to a loss of innocence, as opposed to learning the periodic table. It is unclear whether the Marquise de Merteuil's frequent referral to the seduction of Cécile as the girl's education is entirely an unkind joke. The Vicomte de Valmont participates in this unusual view of education aswell. In Letter One Hundred and Ten, he describes Cécile's recent anatomy lessons in bed with him, in which he has taught her "a sort of debauchee's catechism" ("une espèce de catéchisme à débauche") to help her remember the names of all the important parts. Indeed, Merteuil seems to have a place in her company all picked out for Cécile, once the girl has undergone a few tests and trials (Letter One Hundred and Six):
I had some thought of making a kind of assistant in intrigue out of her, of employing her, as it were, for subordinate roles, but I see that the material is lacking.
(J'avais eu quelque envie d'en faire au moins une intrigante subalterne, et de la prendre pour jouer les seconds sous moi: mais je vois qu'il n'y a pas d'étoffe...)
The education to which the Marquise refers is clearly an education for the stage. In Merteuil's opinion, a woman is made and not born, and she is a character she herself creates. The right material is absolutely essential for the creation of a proper character; without it, a woman cannot control her own fate or her own person. The debauching aspect of this enterprise is, therefore, a necessary precaution.