The ESL network was a communciations channel run by the European Space Liaison, more commonly referred to as the ESL. (TV: An Instinct for Murder)
The Charles de Gaulle was given the designation ESL 1, making it the most important European station. Each channel showed these designations when starting and ending a call. Chief Superintendent David Theroux, stationed aboard the Charles de Gaulle, used the ESL network to make an outbound call to the Pan-Pacific space station, the Coral Sea. The Coral Sea used its own network, which bore its own insignia. (TV: An Instinct for Murder)
During his first days aboard the Charles de Gaulle, Commander Nathan Spring found the lack of gravity unhelpful and distracting. Upon hearing Theroux's suggestion of using an office on Moonbase, Spring used the ESL network to arrange a flight to Moonbase at the earliest opportunity. He was greeted with a "Controller", who took his request. (TV: Conversations with the Dead)
The International Space Police Force also had their own private channel, which was carried by the ESL network, as well as the Coral Sea. Theroux used this to contact Pal Kenzy on the Coral Sea, (TV: An Instinct for Murder) as well as Colin Devis in the ISPF office during an Earthside investigation. Much like on Earth, every computer had a telephone number of sorts. The ISPF office's number was 002 419 164 476 941. (TV: Trivial Games and Paranoid Pursuits)
Shortly before the ISPF's investigation into Santoni-Italia PLC, the new ISPF Personnel Officer reached the ISPF office and informed Spring that he had exceeded the permitted duration of work in space. With the threat of dismissal, Spring begrudgingly accepted to return to Earth for the minimum duration of seven days, for what he called "forced enjoyment". (TV: This Case to be Opened in a Million Years)
The ESL network was also used like an intranet, to store and share files. After the murder of Prof Olivier Devraux, Box was able to access Devraux's files due them being stored on the ESL network. (AUDIO: I Was Killed Yesterday)