It seems like most of Priest's career is built on his defence of dialetheism, but maybe that isn't so surprising when you see just how many issues that notion touches on. The law of non-contradiction is, after all, usually taken to be one of the most fundamental, ineluctable principles of reasoning. Priest does a very thorough job of attacking that notion.
DTL examines in great detail one of the more esoteric debates in philosophy of logic without employing any in-depth formal logic, which keeps it accessible to those who have only minimal training in logic but are interested in understanding a radically different perspective on that deeply important element of our thought, contradiction (I have pretty much zero training in anything outside classical logic, and I could follow the book fine). His deep analysis of Aristotle on contradiction should be interesting for anyone into ancient philosophy.
In my opinion, it's important in philosophy to let no assumption go unchallenged, and DTL is one of those books that absolutely fulfils that goal. This should leave you questioning something you once to took to be obvious common sense.
If you want to delve further into dialetheism, for a more unfavourable analysis of the view, check out the online blog "(Blog&~Blog)". There are over a hundred posts there, and most deal with dialethism & paraconsistency. The book "The Law of Non-Contradiction", edited by Priest, Beall, & Armour-Grab, includes a number of insightful essays from various perspectives (most of which, like this book, are fairly low on formal logic).