Does anything really exist? Sure, we have experiences, which seem confirmed by other experiences, and other people seem to corroborate some of these experiences, so we naively consider the world of our experience as objectively there, but is that all there is to it?
Well, if you go into philosophy with the idea that life is fundamentally sucky and even death doesn't let you escape from that suckiness, so the best thing to do is to somehow get out of it, then you certainly have motivation to try to see things in a different way, and voilà! The Buddha has supposedly gotten ahold of a secret: everything is in fact empty of real being, and with appropriate conditioning, you too can see things that way and so escape this sucky existence, not just in your own mind, but for real and forever! ...But, you probably want to stick around on earth after your Enlightenment and help out the rest of your sick, deluded fellow beings before taking off, okay?
This is the stage upon which entered Nagarjuna in around the 2nd century A.D., a major writer in the earlier stages of the Mahayana Buddhist tradition in India, who was particularly influential on later Tibetan Buddhism and eventually Chan Buddhism in China and its descendant Zen in Japan (and now the West).
Nagarjuna argues that since everything is interdependent (e.g. the observed and the observer, case and effect, opposites, pretty much anything that is in relation to some other thing), then nothing has ultimately grounded, independent being, i.e. nothing meets the criteria for Descartes's view of substance. Instead of taking the tack like Spinoza that therefore there's only one underlying substance, God, Nagarjuna thinks it's more reasonable to conclude that there is no underlying substance at all, that everything is contingent, conditional, and can ultimately be overcome. Moreover, our perception--as Kant says--is conditioned by our habits and expectations. Nagarjuna thinks we can break this conditioning and see the raw flow of experience in a pure manner that will not entail for us the existence of physical objects in an external world. Even the self itself turns out to be illusory; there is ultimately no "I" that is consistent from one moment to the next. Not only should you break your habits of seeing according to these illusions; you also shouldn't cling to philosophical views about these things: even the doctrine of emptiness itself must be overcome.
We'll focus on his "Reasoning: The Sixty Stanzas" and "Emptiness: The Seventy Stanzas," both of which can be found with commentary here.
There are a couple of other readings in that PDF that you might want to skim: "The Good Hearted Letter" lays down a good chunk of the ethical system, which is what the unenlightened folks are supposed to follow to prepare themselves to eventually be able to see the utter emptiness of things.
We'll also skim a work that is sometimes translated as Fundamental Verses on the Middle Way. We found a couple of secondary sources that seemed of great benefit in understanding Nagarjuna:
Jan Westerhoff's Nagarjuna's Madhamaka: A Philosophical Introduction, and David Ross Komito's Nagarjuna's Seventy Stanazas: A Buddhist Psychology of Emptiness.