Where Wizards Stay Up Late : The Origins of the Internet (1998) by Katie Hafner and Matthew Lyon is a book that describes how the ARPANET was built and the people that built it.
It’s interesting to read about how ARPA decided that connecting computers was worth doing and they went out and got BBN to build a packet switched network that was then enhanced by adding more nodes and improving the protocols handling the network. Vint Cerf and Bob Kahn created TCP/IP together which really allowed the network to take off.
The book finally describes how the NSF took over the internet and it expanded in the 1970s and 1980s, being driven by email, FTP, telnet and newsgroups.
If you’re interested in the history of technology it’s definitely a book to read. However, it’s not particularly thrilling and doesn’t have a strong narrative because, it appears, the internet was well constructed and thoughtfully and slowly expanded without great drama.