Books on the history of an airline often seem to cover each major step in IT systems introduction, just like they do for aircraft fleet introductions, so those can be a good source of information.

Back in the big mainframe days the old Sperry Univac company seemed to be to the fore on the hardware side with airlines, later being overtaken by IBM. And many of the initial systems were programmed by the airline's own IT staff (and thus incompatible with each other).

Reservations were usually first (in passing some of the "manual" systems towards their end are fascinating examples of non-computerised systems design and work study in their own right). I believe Indian Airlines (the Indian domestic operator) were still using a mainframe with 80-column punched card input and once-a-day overnight batch update into the 1990s.

A system called Boadicea was the pioneer for BOAC, and an equivalent system called Beacon for BEA, long before they went into British Airways