There was no single inventor. The internet relies on several technologies, digital telephony, local area networks, protocols and routers. The popular applications, like the world wide web were invented later.

Digital telephony was invented by ATT in the late 50s. Before the invention, each telephone was connected to the central office by a dedicated pair of wires. As the number of users increased, the size of cables became unmanageable. To solve this, ATT engineers digitized the analog signal at 56Kb/s. This provided an audio bandwidth of approx 4KHz, which was considered to be sufficient for voice. For normal voice transmission, the analog signal from the customer's telephone was digitized and multiplexed onto the digital trunks. The most common of these was the T1, approx 1.5Mb/s.

ATT also allowed customers to lease a dedicated digital line, with no conversion. The early long distance communication of digital information was done mostly over leased 56K lines.

Local interconnection of digital computers has been done by a variety of technologies. The simplest of these is RS-232, a two wire asynchronous serial communication format, defined in 1960 by the EIA. Maximum speed varies, but is usually 115,000 Kb/s. Other technologies were developed, but many were custom, one-off, proprietary or incompatible. IBM tried to promote Token Ring, a technically superior system that was hard to troubleshoot and install. Arcnet was another system that got popular for a while.

The eventual winner was Ethernet, developed by Xerox PARC around 1973. Its primary designer was Bob Metcalf. It was originally limited to 5Mb/s and ran over thick coaxial cables.

While some organizations used leased digital telephone lines to connect computers over long distances, there was no agreed upon standard that allowed wide interoperability. In 1966, ARPA (Advanced Research Projects Agency), funded by the US department of defense, started work on the ARPANET. The early network used 56K leased lines and originally consisted of a very few computers at universities.

In 1974, TCP, a precursor to TCP/IP, the protocol of the internet was invented. TCP was connected with IP in 1983, producing TCP/IP, the protocol that is still in use today.

The internet was not one invention, it was a series of steps, with many ideas, from many engineers and scientists

Source: I'm a networking engineer who worked with the ARPANET in the 70s