Consequence relations : an introduction to the Lindenbaum Tarski method An in depth study of the concept of a consequence relation culminating in the concept of a Lindenbaum Tarski algebra intended for advanced undergraduate and graduate students in mathematics and graduate students in philosophy as well as researchers in the field of mathematical and philosophical logic. The book is aimed to fill the niche left after the publication of Rasiowa and Sikorskis The Mathematics of Metamathematics (1970) Rasiowas An Algebraic Approach to Non Classical Logics (1974) and Wójcickis Theory of Logical Calculi (1988). The problem of obtaining confirmation that a statement is a consequence of a set of statements as prerequisites on the one hand and the problem of demonstrating that such confirmation does not exist in the structure under consideration on the other hand are considered in a balanced way using predominantly algebraic methods as one two sided problem. Namely for the second part of this problem the concept of the Lindenbaum Tarski algebra plays a key role which becomes even more important when the considered consequence relation is placed in the context of decidability. This role is traced in the book for various formal objective languages. The included exercises are an essential component of the readers assimilation of the books material