Professor Hoppe's book focuses on two main theses. The first thesis is that economic science---and economics is a science---is properly grounded in the deductive method, based on the incontestable axiom of action, explicitly laid down by the economist Ludwig von Mises. Thus, the theorems of economics are true synthetic a priori propositions. Having accepted Austrian economics myself, I find this thesis to be reasonable and uncontroversial.
The second thesis is, for those who already accept the first, a bit more interesting. This thesis states that rationalist epistemology itself---the rationalist philosophy of knowledge---is properly grounded in the axioms of action and argument. Hoppe shows rather convincingly that the two main competitors to rationalist epistemology, namely empiricism and historicism, are incoherent and self-refuting. Furthermore, Hoppe shows how the axioms of action (that human beings act) and argument (that human beings communicate and attempt to convince one another by argument) enable the rationalist to avoid charges of idealism, to which Kant, for example, was vulnerable. This grounding of epistemology in action and argument may seem surprising to some, but Hoppe's argument that it is through action that the mind "interfaces" with the external world is convincing.
Incidentally, Hoppe's rationalist program seems to imply mathematical constructivism; at least he approvingly cites Paul Lorenzen, a mathematical constructivist, though this is somewhat tangential to Hoppe's main arguments. My main problem with mathematical constructivism is its denial of the Law of Excluded Middle---that a proposition P is either true or false and nothing else---though I suspect that constructivists might reply that Gödel's Incompleteness Theorem and its demonstration of unprovable theorems suggests that the constructivists' denial of the Law of Excluded Middle is warranted. But Gödel himself was not a constructivist; he was a mathematical Platonist.
As one might see from the above digression on the philosophy of mathematics, Professor Hoppe's book, though short, has a wealth of ideas to consider. His writing is rather clear with one exception: he tends to write sentences that are considerably long, too long for most people to follow naturally without rereading them or splitting them up mentally. I found myself occasionally experiencing mental stack overflows, as it were, when reading some of Hoppe's longer sentences. Here's an example of a particularly egregious one:
Recognizing, as we have just done, that knowledge claims are raised and decided upon in the course of argumentation and that this is undeniably so, one can now reconstruct the task of epistemology more precisely as that of formulating those propositions which are argumentatively indisputable in that their truth is already implied in the very fact of making one’s argument and so cannot be denied argumentatively; and to delineate the range of such a priori knowledge from the realm of propositions whose validity cannot be established in this way but require additional, contingent information for their validation, or that cannot be validated at all and so are mere metaphysical statements in the pejorative sense of the term metaphysical.
Fortunately, one can mentally "refactor" this sentence into a few separate sentences, and thereby it becomes more digestible. I suspect, though I am not certain, that perhaps these long sentences may have something to do with the fact that English is not Hoppe's first language (that being German). Aside from this, Professor Hoppe presents an intellectually stimulating discussion of the proper methodological grounding of economics and the proper grounding of epistemology. This short volume packs a scintillating discussion on economics, metaphysics, epistemology, action, and argumentation. It's worth reading whether you find yourself in complete agreement with Professor Hoppe or not.
This book is available for free at the Ludwig von Mises Institute. You can also buy a physical copy or Kindle version of it at Amazon.
Professor Hoppe has also written other works that touch on the ideas in this book:
"Intellectual Cover for Socialism"
"In Defense of Extreme Rationalism: Thoughts on Donald McCloskey's The Rhetoric of Economics"
Some of his other writings, though not dedicated to the ideas of this book, also contain discussions of these ideas.