Any discussion of the Liar ought to mention the books of the late Jon Barwise The Liar and Vicious Circles. Also worth mentioning is Raymond Smulyan's lighter puzzle books based on this paradox.

I like the approach of 'paraconsistency' discussed here. But there are some prominent logicians (Girard, for example) who absolutely hate it.

As for "dissolving" the Liar, I would say that it has been dissolved many times, in multiple contradictory ways. Which only goes to show that everything, even logic, can profitably be looked at from divergent viewpoints.