Ra's al Ghul is a well-known character in the Batman mythos. Ask any Batman fan to tell you about Ra's al Ghul and they'll tell you about the League of Assassins, Lazarus Pits and the relationship between Batman and Ra's daughter Talia. One thing that most people don't know is where exactly the origins of these now-iconic details first emerged. The answer is in the Birth of the Demon trilogy.
Ra's al Ghul first appeared in June 1971 in Batman #232 by writer Dennis O'Neal and Neal Adams. He enlisted Batman's help to track down his kidnapped daughter Talia as well as Robin. At the end of the issue, it's revealed that Ra's organized the whole thing to see if Batman was a worthy successor and son-in-law to his daughter Talia, who was in love with him. There is no mention of Ra's immortality or Batman reciprocating Talia's feelings -- that came much later in the "Birth of the Demon" trilogy.
The "Birth of the Demon" trilogy is a collection of three one-shot graphic novels connected by the theme of Ra's al Ghul. These graphic novels are Son of the Demon by writer Mike W. Barr Jerry Bingham; Bride of the Demon by Mike W. Barr, Tom Grindberg and Eva Grindberg, and Birth of the Demon by Ra's al Ghul co-creator Dennis O'Neil and Norm Breyfogle. Though released years apart (1987, 1990 and 1992 respectively) they form a loosely connected story that reveals what we now know as the definitive origins and motivations of Ra's al Ghul.
In Son the Demon, Talia assists Batman in a hostage situation in Gotham which leads to Ra's. Batman decides to join forces with Ra's to stop a terrorist called Qayin but Ra's has a condition -- Batman must embrace the wedding vows he previously made to Talia. Batman surprisingly accepts and officially becomes part of Ra's family. This results in Talia becoming pregnant, but she later tells Bruce she miscarried. At the end of the story, nine months have passed and we learn that there was no miscarriage and that the child was left at an orphanage. This would later inspire Grant Morrison in "Son of Batman" and lead to the creation of future Robin Damien Wayne.
In Bride of the Demon, we are introduced to Ra's desire for an heir. This is often shown as one of Ra's major motivations, not just in comics but in other media as well. Usually, this comes in the form of trying to convince the Dark Knight to join his crusade, often through marriage to his daughter, but Son the Demon saw Batman marry Talia and their son given away. Ra's restores an actress named Evelyn Grace so he can conceive a male heir of his own. This story more openly showed Ra's desperation to continue his legacy and his awareness that continued use of the Lazarus Pits was not the answer, a major point in many modern storylines.
Birth of the Demon provided us with the origin of Ra's al Ghul. Dennis O'Neil and Norm Breyfogle give us the first indication of how long Ra's has lived -- over 600 years. O'Neil and Breyfogle then reveal that Ra's began life as an optimistic physician in a vast city who set out to save those from death. After discovering the Lazarus Pit, Ra's saves a dying prince, but upon emerging from the Lazarus Pit the prince kills Ra's wife. If that wasn't bad enough, the king puts the blame on Ra's to protect his own son and sentences Ra's to a slow painful death locked in a cage with his wife's corpse. Freed by the son of one of his patients, Ra's sets out to recruit his birth tribe and forms a plan to infect the prince with a deadly virus. Ra's then leads the tribe to raze the city to the ground. When all this is done, Ra's declares himself the "Demon's Head" and becomes the man we're all familiar with.
The "Birth of the Demon" trilogy has been stated as taking place on Earth-85, making it an Elseworlds story. However, with the influence it's had on the Batman mythos as a whole, and its role in the creation of Damien Wayne, it's slowly been considered an Elseworlds story that's half canon. After the multiverse shattering events of Dark Knights: Death Metal, the "Birth of the Demon" trilogy and the aspects of it that have become essential to the characters of Ra's and Talia al Ghul can now be considered canon.