This is almost certainly Randall Garrett's Gandalara Cycle (which is actually seven books, but was later republished in three volumes). The first volume The Steel of Raithskar was published in 1981.
The last thing terminally ill language professor Ricardo Carillo remembers is standing on the deck of a Mediterranean cruise ship, watching a giant fireball hurtle toward him. He awakens in the body of a young Gandalaran named Markasset, sharing a telepathic bond with a giant, intelligent feline named Keeshah.
The Steel of Raithskar (1981)
The Glass of Dyskornis (1982)
The Bronze of Eddarta (1983)
The Well of Darkness (1983)
The Search for Kä (1984)
Return to Eddarta (1985)
The River Wall (1986)
- The Steel of Raithskar (1981)
- The Glass of Dyskornis (1982)
- The Bronze of Eddarta (1983)
- The Well of Darkness (1983)
- The Search for Kä (1984)
- Return to Eddarta (1985)
- The River Wall (1986)