Talzin was Maul's biological mother. As a child, Maul was taken from her by Palpatine so he could be trained as a Sith. Years after his defeat on Naboo, Talzin sent her other son Savage Opress to find Maul. Once Savage brought Maul home, she used her own magic powers to restore his legs, memory, and sanity.
Talzin cared deeply for her son, treating him with love and kindness, and valuing him above all others. She ultimately cared more about Maul than her own self, as she willingly sacrificed herself to allow Maul to escape from Palpatine and his minions. Talzin's love and protectiveness for Maul was reciprocated, and Maul was greatly devastated by her death.
Even after sixteen years, Maul still held an extremely bitter grudge against Palpatine for his actions against him and his mother.
Maul and Savage were born to the same Nightsister, Mother Talzin herself, along with a third, younger brother, named Feral (later killed by a transformed Savage on Asajj Ventress's orders). Maul was taken from his family by Palpatine and trained to be a Sith Assassin. Maul would be reunited with his brother when Savage arrived on the junk planet Lotho Minor, where Maul had hidden himself after his defeat in the Battle of Naboo. After Savage found him, the Nightbrother was taken back to Dathomir and had his legs, memory, and sanity restored by Mother Talzin. Afterwards, Maul took Savage as his apprentice, and began teaching him the ways of the Sith.
Despite the hierarchy Maul had created between them, the brothers did care deeply about one another, allowing them to work together as an efficient team. Together, using this bond and Maul's training from Palpatine, the two Zabraks set out to create their own Sith Empire. Unfortunately, this drew the attention of Palpatine, who branded them rivals. When Palpatine killed Savage, Maul was devastated and tried to avenge him, but Palpatine was too powerful. With his last breath, Savage decreed himself an unworthy apprentice, saying that he wasn't like Maul and never was, further adding to Maul's grief.
The memory of Savage's death was painful enough that sixteen years later, Maul mentioned it to Ezra Bridger as one of the reasons he wanted the Galactic Empire to fall.
Darth Maul and Obi-Wan have been archenemies since the Battle of Naboo. When Maul killed Qui-Gon Jinn, Obi-Wan fell on him with a relentless barrage, eventually defeating him by cutting him in half and sending him plunging into the depths of a reactor shaft. Maul kept himself alive with his rage and the Force at the cost of his sanity.
After his sanity was restored by Talzin, Maul became determined to get his revenge on Obi-Wan. His hatred of Obi-Wan also grew ever stronger when the Jedi struck a nerve upon saying that he understood why Maul turned to the Dark side and mentioning where he came from. With help from the Mandalorian Death Watch, Maul took over Mandalore and killed his former lover Satine Kryze to cause Obi-Wan pain.
Following the rise of the Empire, Maul believed Obi-Wan dead, but upon seeing he lived from images revealed by merging Holocrons with aid from Ezra Bridger, Maul was both surprised and delighted. In "Visions and Voices", Maul learned through a Nightsister ritual, that Obi-Wan is on the planet Tatooine, and is eager to get revenge on his old nemesis once and for all.
During the Siege of Mandalore, Maul and Ahsoka had a direct confrontation, in which Ahsoka briefly managed to capture the former Sith, but chose to save Rex instead of killing him. Many years later, they came face-to-face once again on Malachor. Maul thinks little of Ahsoka as evidenced by him calling her things like "Part-timer" and "Lady Tano" in mockery of her departure from the Jedi Order.
When he learned that the Death Watch considered Obi-Wan Kenobi an enemy, Maul allied with Vizsla and together they created the Shadow Collective. When the Collective was formed, Maul had the gangsters it was composed of to attack key places on Mandalore to turn the people against Duchess Satine Kryze and then sent the Death Watch to stop the thugs to win the people over. After Satine was overthrown, Vizsla betrayed Maul and the Collective to assume leadership of Mandalore. Fortunately thanks to Savage, Maul anticipated this and challenged Vizsla to a duel according to the rules of Mandalorian Code for leadership of Death Watch during which he killed Vizsla, beheading him, and assumed leadership of both Death Watch and Mandalore.
Despite the fact both are part of the same Night Clan, lead by Mother Talzin, Maul and Ventress are mortal enemies.
Maul and his successor have been enemies since his mind was restored by his mother due to hating each other. Maul hated Dooku for being his replacement as Sidious's apprentice and Tyranus hated Maul for being a threat to him. They also didn't regard each other as a true Sith Lord; Tyranus saw Maul as nothing more than an animal and Maul saw Dooku as a pretender.
Palpatine took Maul as an infant from his mother. While still apprenticed to his own master Darth Plagieus, Palpatine trained the Nightbrother in the ways of the Sith. Maul was originally loyal to Palpatine, obeying his every command without question. Maul and Palpatine's bond as master and apprentice originally was strong enough that Maul knew about the plan to instigate the Clone Wars, as he expressed disappointment upon finding it had begun without him. When Obi-Wan Kenobi defeated him on Naboo, Palpatine replaced Maul with Count Dooku, who became Darth Tyranus. The fact that he had failed and was replaced drove Maul into madness for more than a decade. Palpatine's betrayal caused Maul to discard his loyalty to the Dark Lord of the Sith, vowing to eventually overthrow him.
Maul met Palpatine once again years later on Mandalore. However, despite his new-found hatred for his former master, Maul still greatly feared Palpatine, referring to him as "the most powerful being in the galaxy". Upon sensing his presence on Mandalore, Maul's initial reaction was fear, then feigned respect and devotion to try and win back Palpatine's favor. Palpatine saw through the ruse, branding the two Zabraks a rival splinter faction of the Sith Order and taking him captive after killing Maul's brother, Savage Opress and defeating Maul in a duel. After he escaped and witnessed the death of his mother at the hands of Palpatine's minion General Grievous, the Zabrak fled, no longer considered a threat or a Sith Lord. Sometime later, Maul learned of Darth Plagueis and came to realize he was never considered an actual Sith Lord by his former mentor, only a tool of Palpatine's will.
Maul eventually came to Malachor after years of evading the Galactic Empire in order to retrieve the Sith Holocron hidden there so that he could use it to exact revenge on Palpatine and Darth Vader (whom he had learned of during his years of running and hiding from the Galactic Empire and its Inquisitors). This plan was thwarted when Ezra Bridger and Kanan Jarrus claimed the Holocron and escaped.
Although it is unknown if they have ever met in person, Maul counts Vader as his enemy. Maul has continually evaded Vader, knowing fully well that he does not have the strength needed to successfully fight Vader alone on equal terms.
Maul is enemies with the Dark side Adepts known as the Inquisitors. Maul has at present also killed two of them; the Seventh Sister and the Fifth Brother (he may have also killed more). Maul is also more than a match for any Inquisitor to cross his path.
Maul is the enemy of Kanan Jarrus due to both his desire to make Kanan's apprentice, Ezra Bridger, into his apprentice, and because of his past actions against the galaxy and the Jedi. Maul and Kanan's enmity was strengthened when Maul blinded Kanan on Malachor and through Kanan's subsequent defeat of Maul.
Ezra Bridger was tricked by Maul during their mission to Malachor into trusting him, paving the way for a potential master-apprentice relationship between the two. Maul also had an effect on Ezra with his words, causing him to begin to believe that to fight his enemies, he needed to think like them. Though Ezra currently sees Maul as an enemy and blames him in part for the supposed death of Ahsoka Tano, Maul still currently believes that Ezra may yet join him.