Roswaal L Mathers/Relationships

Echidna
Years before the Great Calamity, Echidna encountered young Roswaal who was unable to utilize his insane magical talent and potential and was being treated as a sickly nuisance by everyone who encountered him as back then, magic was very much misunderstood and mages weren't as renowned as they are now (with few exceptions). Echidna sensed his ability and potentially devastating power and decided to take him under her mentorship, teaching him how to properly use magic and opening Roswaal's eyes, allowing him to recognize that his body isn't a "danger" but a "gift", allowing him to prevail and learn how to effectively use all six magical elements. As a result, Roswaal harbored intense and deep feelings for her, which were unfortunately very one-sided as Echidna is unable to comprehend human emotions. She was the most important person to him. After her death, Roswaal became obsessed with reviving her, even being prepared to give his life in order to achieve his desired future, kill the Dragon and cross paths with Echidna once more.

Beatrice
Both of them are acquainted with each other for more than 400 years, as they were both under Echidna's mentorship and protection. Before Echidna's demise, Beatrice formed a pact with her and vowed to protect the Forbidden Library located in Roswaal's Mansion. After Echidna's demise, Beatrice shut herself into the library, spending all of her time in there. Despite that, Roswaal still kept on visiting her, even after the original Roswaal A Mathers "died". Tappei later confirmed Roswaal loved Beatrice and deeply cherished her and the relationship they had, despite Beatrice distancing herself. Although as expected, he would sacrifice her for his grand goal, despite the fondness he had of her. His only regret is how cold her attitude is towards him.

Ram
Roswaal took in Ram and Rem under his wing and is shown to deeply care for their well-beings. Oftentimes using Ram as an informant on matters, their mutual trust becomes evident. Despite this, he has no qualms on sacrificing her to meet his goals as shown in Arc 4, where he kills Garfiel, despite Ram being in the way in one loop. It is worth noting however that he knew he was going to die, and that Subaru would loop to bring her back anyway.

However, it is shown that he is emotionally attached to her as well as in Wrath "If" when Ram dies and Roswaal lives, Roswaal falls into a state of despair and feels incomplete without her. This implies that he may return her feelings to an extent.

Rem
Roswaal took Rem and Ram under his wing and was shown to deeply care for them, as seen when Rem died of unknown causes and he immediately suspected that Subaru is responsible (he was even prepared to kill him, much like Ram).

Emilia
Emilia's benefactor and backer in her bid to acquire the throne. He's considered an odd lord, especially due to his fondness for demi-humans like her to the point where he would hire them. In truth, he is only actually using her to control Subaru and coerce him into using Return by Death to fulfill his ambition of reviving his late master through the wits of his Gospel. To do so, he needs a guaranteed way to put Emilia on the throne because he has no faith in Emilia's resolve to overcome her past and deeply-rooted hatred of the Witch of Envy. However, with the encouragement and support of Subaru and several others, Emilia shatters his expectations by passing all 3 of Echidna's trials. He is then forced into backing her earnestly.

Natsuki Subaru
When they first met, Roswaal appeared to be genuinely grateful for Subaru rescuing Emilia's insignia, even offering him anything he wants as gratitude. He appears to be rather friendly to the young boy. However, Roswaal is more than prepared to kill Subaru in one of the loops, connecting him to be the cause of Rem's unknown death.

In Arc 4, their relationship became rather antagonistic (i.e. giving Subaru half-truths or intentionally throwing monkey wrenches in the latter's plan). Roswaal becomes aware of Subaru's "Return by Death" and later admits that he's molding Subaru to become like himself (acting on his own desires rather than waste time saving someone's life). By the climax of said Arc, Roswaal and Subaru have placed a bet, which he lost (although he will force Subaru to use Return By Death, should he make a mistake).

Hector
Hector and Roswaal used to share an extremely hostile relationship. Roughly 400 years ago, Hector pursued Echidna and located her at her hideout in the Sanctuary. Roswaal faced off against him, trying to fend him off and protect the Sanctuary but he failed miserably, being one step away from death. At the last second, Echidna came to the rescue, saving Roswaal's life but at a cost of his ego being utterly shattered. In the following years after his defeat, Roswaal started wearing the same clothes and talk in the same manner as Hector, in order to not forget the humiliation he suffered all those years ago.