"Critical reasoning" and "argumentation" are two labels, which are now utilized in academia to generally refer to subject matter I originally studied as informal logic, particularly "informal" fallacies. "Critical thinking" is, to a large extent, a 21st Century modernization of Aristotelian logic.
The eight chapters in the table of contents in Douglas Walton's book provides an excellent formulation to address eight essential elements of critical reasoning in argumentation. Reviewing Douglas Walton's table of contents provides an excellent outline and overview on which to orient one's critical conceptualization of any particular issue - in this regard, Douglas Walton's table of contents is much better analytical overview than provided by the table of contents of either of the two books noted below.
AMAZON.com's listing for Douglas Walton's FUNDAMENTALS OF CRITICAL ARGUMENTATION has AMAZON's "Look Inside" feature - so, prospective customer, take a "look inside" at the table of contents of this Douglas Walton book, which illustrates my contention about its value as an overview and useful analytical tool.
There are two other books in the field of critical reasoning and argumentation which are comparable to Douglas Walton's book, but which have their own individual strengths: a hardbound book titled CRITICAL THINKING: A CONCISE GUIDE, by Tracy Bowell and Gary Kemp; and a paperback book titled GOOD REASONS FOR BETTER ARGUMENTS: AN INTRODUCTION TO THE SKILLS AND VALUES OF CRITICAL THINKING, by Jerome E. Bickenbach and Jacqueline M. Davis. I have both of these books, as well as Douglas Walton's book, and I consult them all, for the different perspectives they offer.
The commonality of these three books is that critical reasoning always boils down to evaluating the reasoning involved in the context of any one particular individual argument - and in providing intellectual tools for "SPOTTING fallacies" in the reasoning of others, or in the reasoning of oneself.
Of the three textbooks on the subject of "critical thinking/critical argumentation" of which I am aware, two (including this one) are authored by Canadian university professors, and one is authored by a Scottish and a New Zealand university professor. Has this subject caught on in the U.S.?
The Birkenbach and Davis book, because it is a paperback, costs half the price of either of the two hardbound books. If you are a neophyte in the subject of "critical thinking," this book is a good starting point for a quest into the "critical argumentation" field.
As I learn, I am conscious of finding myself gravitating to an increasing overall preference for Douglas Walton's FUNDAMENTALS OF CRITICAL ARGUMENTATION (2006), in contrast to the other two books noted above, which still remain good and valuable works.