If it's named, and isn't mentioned as "unsound" then it is mainline.
Main-line openings

Thank you.
So basically, a main-line opening is one of the many named openings which have come into being eg Giuoco Piano, French Defense, Sicilian, King's Gambit, but not one of the many variations of any of these?

daswann: I think that's close but not quite there.
In the context of that recommendation, a main line opening would be the Ruy Lopez, the Queen's Gambit, the French, Caro-Kann, Sicilian, etc.
The "19th century gambit openings" would probably include the Blackmar-Diemer Gambit, the King's Gambit, the Center Game, the Ponziani Opening, the Danish Gambit, the Evans Gambit.
I think the point is that when you are learning, it is not necessary to play a "respectable" opening, or "mainline" opening, because there are important aspects to the game that you can only learn by playing the gambit openings.
Perhaps I should start playing them too! :-)

If it's named, and isn't mentioned as "unsound" then it is mainline.
That's wrong. Here's an example. The Open Sicilian is considered the "main line" of the sicilian defense as it is white's most critical try for an opening advantage. Practice has shown that this move is white's best chance to get something against 1...c5. It produces sharp imbalanced games where the better play can play for a win. Thus it is the move most often played by the top players and is considered the "main line". Other named choices for white are not considered the main line, such as the Alapin, the Closed Sicilian, or the Grand Prix attack. These openings however do have their own main lines and sidelines, so for example you can play a mainline opening like the Ruy Lopez, but then disappear into an offbeat sideline at a later date.
As for early moves, openings like the Ruy Lopez, the Scotch, the Queens Gambit, the Sicilian, the Petroff etc are considered "main-line openings", whereas openings like the polish, the grob, most gambits, the st. george, are considered non-mainline, and some like the polish or the grob are considered "offbeat".
I have not been playing chess for very long and have come across the guidance below:
"Most junior players seem to benefit from going through a phase of playing classical 19th century open games and gambits, to develop tactical ability and awareness of the importance of "the initiative", but sooner or later it is important for an ambitious player to start playing main-line openings - there is usually a good reason why they are main lines!"
What are main-line openings?
Thanks
Deborah