Based on Economic Science and the Austrian Method by Hans-Hermann Hoppe.
This book is very dry and difficult reading, as bad as Mises "Human Action", though thankfully much shorter, or I never would have read it, as I never finished "Human Action".
The Austrians try to base everything on fundamental ideas, what they call "synthetic a priori" after Kant; I have never read Kant so I can't tell you whether their claim that their ideas are Kant's "synthetic a priori" or not; but they are the same types of ideas I have been calling for years "undefinable primitives". These ideas that they try to base everything on, "action", "value", "cause and effect" aren't some mystical information from nowhere, which is what earlier reading about Kant had suggested he thought - I think they are ideas absorbed from observation of reality and how humans act (and, unfortunately, what people have absorbed through reading and stories, which is why so much "intuition" on larger issues where people don't have direct experience is often so irrational), but they are so basic that they are hard even to discuss intelligibly, much less define.
A second part of the Austrians' disagreement with conventional economics is based on the supposed differences between human motivations and interests and the natural world - "the impossiblity of causal predictions in the field of human knowledge and actions" (p.43). Human preditions must be based on actions and goals, and what the particular human knows at the time he chooses his actions and goals. The particualrity of what a human knows is another reason they dislike and distrust statistical knowledge, like the GDP, it loses too much necessary information.
"... empirical knowledge which is based on understanding - just as according to our intuitions economic propositions claim to be based on understanding - rather than on observations." (p.57) Actually, as I suggested above, our intuitions and understanding are based on internalized observations and knowledge received from others.
"In explicitly understanding knowledge as displayed in argumentation as a peculiar category of action, it becomes clear immediately why the perennial rationalist claim that the laws of logic - ... - are a priori true propositions about reality and not mere verbal stipulations regarding the transformation rules of arbitrarily chosen signs, as empiricist-formalists would have it, is indeed correct." (p.71)
A part of Hoppe's argument in the book is a misguided (in my opinion) attack on a sort of naive empiricism that I have never actually encountered. I haven't read much technical economics literature, so it's possible some economists are making these sort of shallow mistakes, but what I have read in economics suggests this is unlikely.
Another part of his argument is an attack on historicism in economics, I think this is even more misguided, without historical knowledge Austrian economics could not have been developed. Also, some of the best economic reading I have done has been by Thomas Sowell, an economic historian. Another good economics writer is David D Friedman, a non-economist.
The best part of Austrian economics is that they give a clear rational account of the few things nearly all economists agree on: minimum wages increase unemployment, wage and price and rent controls cause other (non-price) forms of rationing, and so on.