  During his brief life, the Polish mathematician and logician Adolf Lindenbaum
(1904--1941) contributed to mathematical logic, among other things, by several
significant achievements. Some results of Lindenbaum's, which bear his name,
were published without proofs by other people from the Lvov--Warsaw School and
the proofs later were provided by some others, though the authorship of
Lindenbaum has never been challenged. Many may have heard about Lindenbaum's
lemma, asserting the existence of Lindenbaum's extension, and Lindenbaum-Tarski
algebra; less known is Lindenbaum's logical matrix. This tutorial is devoted to
the two last concepts rather than the first one. However, the latter can be
understood in a purely algebraic fashion, if one employs the notion of
Lindenbaum-Tarski algebra. In general, the notions of Lindenbaum matrix and
Lindenbaum-Tarski algebra have paved a way to further algebraization of logic,
which had been begun by George Boole in the 19th century, as well as to a new
branch of logic, model theory. For this reason, the present tutorial is also a
gentle introduction to algebraic logic.
  A uniting idea of the aforementioned concepts is a special view on the formal
judgments of a formal language. It is this view we call the Lindenbaum method.
Although Lindenbaum expressed merely a starting viewpoint in the tradition of
Polish logic of the time, this viewpoint became a standard ever since and its
development goes on until this day, continuing to shape the field of algebraic
logic. Our main objective is to demonstrate how this view gave rise to
formulating the aforementioned concepts and how it opens door to unexplored
paths.
