The Trivium method: (pertains to mind) – the elementary three. General Grammar,  Formal Logic,  Classical Rhetoric
 LOGIC — (Answers the Why of a subject.)
Developing the faculty of reason in establishing valid [i.e., non-contradictory] relationships among facts yields basic, systematic Understanding- it is a guide for thinking correctly; thinking without contradiction. More concisely, it is the art of non-contradictory identification. The work of logic is proof. Proof consists of establishing the truth and validity of a concept or proposition in correspondence with objective, factual reality by following a self-consistent chain of higher-level thought back down to foundational, primary concepts or axioms (i.e., Existence, Consciousness, and Causality). It is a means of keeping us in touch and grounded to objective reality in our search for valid knowledge and understanding. Logic brings the rhythm of the subjective thoughts of the mind, and the subsequent actions of the body, into harmony with the rhythm of the objective universe. The intention is to amicably synchronize individual mental processes, and their attendant actions, with the processes of our surrounding natural, factual existence over the period of a lifetime.
Logical Fallacies (common types of errors in reasoning):
Fallacies are broken down into two categories: formal and informal. Formal fallacies are based strictly on the logical formation of an argument (deductive). Informal fallacies, which are the most commonly recognized and easiest to learn, take into account the non-logical content of an argument (inductive); they are false for epistemological, dialectical or pragmatic reasons, and typically fall under three categories: relevance, presumption, and ambiguity. The first formation of logical fallacies comes to us from Sir Thomas Aquinas and “The Scholastics”.
Study Notes: Download
The Trivium Method with Gene Odening, Gnostic Media Podcast episode #049 (start here)
Informal fallacies with Dr. Michael Labossiere, Gnostic Media Podcast episode #062
Dr. Michael Labossiere – 42 most common informal fallacies: http://www.nizkor.org/features/fallacies/
List of 90 informal fallacies – http://www.don-lindsay-archive.org/skeptic/arguments.html
Extensive list of informal fallacies – http://changingminds.org/disciplines/argument/fallacies/fallacies_alpha.htm
Fallacies by their Latin names – http://changingminds.org/disciplines/argument/fallacies/fallacies_latin.htm
Formal and informal: (Intermediate to advanced)
Taxonomy of Logical Fallacies
Other study material:
Peikoff, Dr. Leonard, Introduction to Logic, audio, Order here – This series is very informational for getting started and is best studied before The Trivium by Sister Miriam Joseph.