The Dance of Dragons, A True Telling is a history book about the great civil war in the Seven Kingdoms known as the Dance of the Dragons, fought between two rival branches of House Targaryen, one led by Rhaenyra Targaryen and the other by her half-brother Aegon II Targaryen. It was written by Grand Maester Munkun, who lived through the war.
In the books
In the A Song of Ice and Fire novels, it is noted that Munkun's history contains some inaccuracies, such as indicating that the dragon that killed Ser Byron Swann was Vhagar, when in fact it was Syrax. Vhagar was ridden by Prince Aemond Targaryen, a brother and supporter of Aegon II Targaryen, and House Swann was among the supporters of Aegon II; therefore, it is unlikely Ser Byron attempted to kill Prince Aemond's mount. Meanwhile, Syrax was ridden by Aegon II's rival, Rhaenyra Targaryen herself.
Munkun's work was said to be biased in favor of Rhaenyra, in contrast to the history written by Septon Eustace, which was biased in favor of Aegon II.
The World of Ice & Fire reveals that Munkun was a member of the council of seven Regents that ruled the Seven Kingdoms after the death of Aegon II, as his successor, his nephew Aegon III Targaryen, was still a child. Munkun was the only member of the council that held office from 131 AC to 136 AC, when the council was dissolved. Munkun would also hold the office of Hand of the King.
The name of Munkun's book in the novels is actually "The Dance of the Dragons", not "The Dance of Dragons" - leaving out "the" from the title - which is what Shireen calls it twice in the TV episode. For that matter, the name of the war itself is "The Dance of the Dragons", the book title is simply quoting it. The Season 5 TV episode that Shireen says this in is also called "The Dance of Dragons" - omitting "the" without explanation. Given that other materials from the TV continuity such as the Histories & Lore videos have already clearly referred to the conflict as "The Dance of the Dragons", it appears that this remains the canonical name as it was in the novels, and that the dialogue in episode 5.9 is simply in error (probably a script error, not just the actress misspeaking, because she said the name twice). Something similar happened in Season 2: the first time that a name is stated for the conflict between the Starks and Lannisters, Tywin says it is being called the "War of Five Kings" - omitting "the" - but later episodes prominently and repeatedly called it "the War of the Five Kings". Therefore this article assumes that the full title of Munkun's book is the same as it was in the A Song of Ice and Fire novels. Characters in episode 5.9 might have just been referring to it without "the" in the title as a clipped form of the name, but the scripwriters' intent is unclear - otherwise the two variant names seem interchangeable.