In which book of the Bible is the birth of Jesus told? Is it Matthew or Luke?

Both, actually.

For Christians, the authoritative accounts [on the birth of Jesus] are those given in the Gospel of Matthew and the Gospel of Luke that form part of the New Testament of the Bible. More elaborate accounts of the events relating to the birth of Jesus have also been preserved, but they have not been included in the Christian canon of the Bible. The Gospel of Mark, arguably the earliest of the canonical gospels, is silent on the nativity."

https://en.wikipedia.org/wiki/Nativity_of_Jesus

Both - the book of Matthew tells Jesus' lineage, and gives a briefer summary of the birth than Luke does. Luke is the more familiar passage - "she brought forth her firstborn son and wrapped him in swaddling clothes and laid him in the manger, because there was no room for them in the inn."(Luke 2:7) "Glory to God in the highest, and on earth peace, goodwill toward men" (Luke 2:14) If you've ever heard the Christmas story read, Luke is usually what you'll hear.