R+L=J is probably one of the most well-known and popular theories amongst ASOIAF readers and one that I personally believe in.
The theory is that Jon Snow is not the bastard son of Eddard Stark like everybody believes and is instead the son of Rhaegar Targaryen and Lyanna Stark.
Lyanna Stark is the deceased younger sister of Eddard Stark, older sister of Benjen Stark and aunt of Robb, Sansa, Arya, Bran and Rickon. She was betrothed to Robert Baratheon and was one of the causes of Robert’s Rebellion aka the War of the Usurper in which Robert Baratheon was the victor and was crowned King of the 7 Kingdoms. She died towards the end of Robert’s rebellion shortly after reuniting with Ned, dying in his arms.
Rhaegar Targaryen is the deceased older brother of Daenerys and Viserys Targaryen and the son of Aerys II Targaryen more commonly known as the Mad King. Rhaegar’s abduction of the then betrothed Lyanna Stark was one of the key events that led to Robert’s Rebellion.
Tourney at Harrenhal:
The first time that Lyanna and Rhaegar met was at the Tourney at Harrenhal held by Lord Walter Whent in 280 AC (Aegon’s Conquest). Lord Whent offered rewards three times greater than those offered by Tywin Lannister in the Anniversary Tourney at Lannisport in 272 AC which attracted many challengers.
Rhaegar Targaryen emerged as the champion of the joust and crowned Lyanna Stark as the Queen of Love and Beauty, crowning her with a crown of blue winter roses(commonly associated with Lyanna) which was scandalous as Rhaegar was married to Elia Martell who was present at the tourney and Lyanna Stark was betrothed to Robert Baratheon.
Abduction of Lyanna Stark:
The official version goes that about a year after the tourney at Harrenhal, Lyanna was abducted then raped by Rhaegar who kept her prisoner in the Tower of Joy located in Dorne. The theory goes that Lyanna did not get abducted, instead, she ran away with Rhaegar to Dorne as the two were in love.
One piece of evidence which suggests that the latter is likely the case is that Lyanna was "wolf-blooded" - headstrong, willful, courageous and hot-tempered, like her eldest brother, Brandon Stark, which makes her abduction improbable. Another thing to note is that she is constantly compared to Arya Stark, a tomboyish character by Eddard in terms of personality and looks, he even mentions that if his father allowed it, she would probably carry a sword. One occasion was during the tourney of Harrenhal where she found Howland Reed, father of Jojen and Meera Reed, being bullied by 3 squires and attacked them with a tourney sword. Would a girl as fierce as Lyanna get abducted so easily? Probably not.
After Lord Tyrell and Lord Redwyne bent their knees and swore fealty to Robert, Ned rode to the Tower of Joy in Dorne with 6 companions, where Lyanna was being held captive and was met with 3 kingsguard guarding the entrance to the Tower of Joy. At that point in time, take note that Rhaegar Targaryen had already been slain by Robert in the Battle of the Trident. In the end, only Howland Reed and Eddard Stark survived the ensuing battle. Ned found Lyanna lying in a “bed of blood”, dying. When Eddard recalls the conflict in a dream, there is an additional detail. While the combatants clash, Lyanna screams. The dream then switches to a storm of blue rose petals, blowing across a blood-streaked sky. It is uncertain if these details are accurate memories. Lyanna’s final words were “Promise me, Ned” while she lay dying in the arms of her brother.
Firstly, why would 3 members of the kingsguard be guarding Lyanna when they should be protecting the 2 remaining children of King Aerys II, Daenerys and Viserys Targaryen ? Could it be that they were guarding Lyanna, knowing that she was about to give birth to Rhaegar’s son and therefore the heir to the Iron Throne ?
Secondly, the “bed of blood” could mean childbirth which is further supported by Lyanna screaming as the combatants clashed. She could have gone into labour as the fight was raging on. As I previously mentioned, she was a “wolf-blooded” girl so it is unlikely that she screamed if she saw a battle taking place although as stated, the details may not be accurate.
Finally, what does her last words, “Promise me Ned” mean? It could be that she made Eddard promise to take Jon home and raise as well as protect him as his own child so that the truth of Jon’s parentage won’t be revealed and so Rhaegar and Lyanna’s son wouldn’t have to face Robert’s wrath. Robert had both of Rhaegar’s children with Elia, brutally murdered as they too have a claim to the Iron Throne and could stir up trouble if they were left to live. Robert would likely have Jon killed as he would pose a threat if he had discovered his true parentage even if Robert did love Lyanna.
Eddard Stark is known to be a painfully honour-bound man. Yet the book would have us believe he would father a bastard son and return to Winterfell with him which is considered a huge slap in the face to his wife, Catelyn Stark which he loved.(Yes, at this point he was already married). He also has never disclosed Jon Snow’s mother’s identity and refuses to speak about her to anyone, even to Jon only mentioning that her name is “Wylla” to Robert in passing, not even describing how she looks like which is rather fishy. He then uses the pretence that adultery is a dishonour on both him and his wife which is why he didn’t want to talk about it. So why would he go out and father a bastard?
Jon is said to closely resemble Arya Stark who as I previously mentioned, is said to look a lot like Lyanna Stark. This could mean that the books are hinting indirectly that Jon looks like Lyanna which may point to Lyanna being his mother.
The books also mention that Eddard had “lived his lies for fourteen years”. Jon Snow, at the start of the books, is 14 years old. This could point to Jon being his lie. In the eighth Eddard chapter of A Game of Thrones, Ned contemplates the significance of King Robert’s bastards and his thoughts drift to Jon Snow, his own bastard then drifts to Lyanna Stark, followed by his promise to her and finally, Rhaegar Targaryen. This implies that there is some sort of link between these 3 individuals.
Also, while the other Stark children’s direwolves are described as having dark fur, Jon’s direwolf, Ghost, has white fur. White is a colour commonly associated with Targaryen features.
While in the House of The Undying, Daenerys has a vision of Rhaegar holding his newborn son, Aegon, proclaiming that “there must be a third” as “the dragon must have three heads”. According to Jon Connington, Elia, Rhaegar’s wife, was believed to be infertile after 2 difficult pregnancies, and that Aegon the Conqueror himself had 2 wives. It is logical for Rhaegar to have attempted to fulfil the prophecy by having a third child with another woman.
Another vision seen by Daenerys is one of “a blue winter rose, growing from a chink in a wall of ice, filling the air with sweetness”. Blue winter roses are commonly associated with Lyanna Stark as she was very fond of them and Ned associates them with her death. Jon, who may be her son, is currently at the wall which explains the wall of ice.
When Catelyn Stark suggests to Ned to take Jon South, he panics, using the pretence that people would be cruel as Jon is a bastard. This could be because of his oath to Lyanna and that Eddard was afraid of Jon being near Robert and incurring his wrath should he let it slip that Jon is Rhaegar and Lyanna’s son.
Eddard has also openly opposed to the killing of Targaryen children for their blood which could be because of his protection of Jon. He even opposed to Robert’s idea of killing Daenerys and Viserys which endangered him greatly and put strain on his friendship with Robert.
Last of all, why name the book series “A Song of Ice and Fire”? If R+L=J is true, that would make Jon the personification of “A Song of Ice and Fire” as Starks are commonly associated with winter, ice, cold, direwolves etc. and Targaryens are commonly associated with fire, dragons, blood etc.