Back when I was in school, I had to read The Black Cauldron. I don't remember it very well, but I do remember liking it a lot. I liked it enough that I bought the first book, too. I was planning on getting the other ones and reading all five, but it's seven years later and I never did get them. So I figured I might as well read The Book of Three now (especially since it's a shorter book and I'm on a quest to read 50 List books this year).
Unfortunately, The Book of Three was nowhere near as good as The Black Cauldron. I found Taran to be super annoying throughout at least two-thirds of the book, which made it super hard for me to read. So what should have taken me maybe two or three days to read ended up taking double that.
The Book of Three is the first of Taran's adventures. Taran dreams of adventure and being a hero. When Hen Wen the Oracular Pig runs off, Taran, the Assistant Pig-Keeper, heads off after her. In his quest to bring her home, he encounters all of his friends for the first time, notably Prince Gwidion, Gurgi, Eilonwy, the bard Fflewddur Fflam, and Doli. All the while, Taran complains about everyone (especially Gurgi and Eilonwy, both of whom are extremely helpful) and makes multiple bad decisions that almost repeatedly get the group of them killed (Gwidion isn't with them at this point - they believe he perished in Spiral Castle, which is where Taran met Eilonwy and the bard. Taran actually blamed Eilonwy for his death at one point because she rescued Fflam instead of Gwidion, but it was Taran who insisted she rescue the man in the other cell because he assumed it had to be Gwidion).
I understand that The Book of Three was all about Taran having his first adventure and growing up a bit because of it (and he actually did mature a bit by the end). But honestly, if I had read The Book of Three before The Black Cauldron, I would never have picked up the second book. As it stands, The Book of Three turned me off of the Chronicles of Prydain.