The book spends almost half of its length discussing Ada's parents, Lord Byron and Lady Byron (aka Annabella Milbankee, Baroness Wentworth). This is worthwhile, as it sets up some of the currents that flow through Ada's life, at least in this telling of the story (and I'm in no position to contradict it). Byron of course is the great romantic poet of the age (or any age, possibly), and Annabella was something of a mathematican herself, being called (somewhat cattily by her husband) the Princess of Parallelograms. The two separated shortly after Ada's birth (a certain coolness developed after she learned he was boinking his own half-sister) and it was quite rancorous, and society had to choose sides. On the whole, Annabella got the sympathy of most, while Byron went on being Byron and was soon out of the country, and dead within a few years in Greece.
And from then on, Ada was something of an outlet for Annabella's desire to be the wronged one in the relationship, and simultaneously, Ada had to be protected from romantic impulses, and pushed towards math and science. This worked up to a point, but... well... as a teenager Ada ran off with her tutor... so there were some strong romantic impulses there as well, it would seem.
Ultimately, Ada was found a husband that she didn't have much use for, but produced a passel of children before being pretty remote from her husband. She was further instructed in math by De Morgan, whose wife was among Annabella's coterie, who all spied on poor Ada relentlessly. But getting married got her a bit out from her mother's thumb, and she could pursue her own interests. She became acquainted with Charles Babbage, and it is this association for which she is best known. Babbage gave a lecture on his early computer ideas in Italy, which was published in French. Ada was chosen to translate the published lecture into English. Along the way, and with Babbage's encouragement and help, she added annotations to the lecture that turned out to be twice as long as the lectures themselves. Among these notes were a 'computer program' for calculating Bernoulli numbers that could be run on Babbage's designed (but never built) computer.
For this, Ada is sometimes credited as the first computer programmer. But although the first 'computer programs' were published under her name, there is little doubt that Babbage had provided a great deal of the raw material, if not the entire programs. But more to her credit, in some of her other notes, she seems to have seen quite clearly further into the Information Age than even Babbage, and understood the vast potential and flexibility of the 'computer'.
Babbage's computer came to nothing at the time, so Ada had no chance to really pursue that, and as things turned out, she had no chance to pursue much of anything. Uterine cancer, laudanum, and fast living led to her death in her mid-30s.