Formal Concept AllalY.5is is a field of applied mathematics based on the math ematization of concept and conceptual hierarchy. It thereby activates math ematical thinking for conceptual data analysis and knowledge processing. The underlying notion of "concept" evolved early in the philosophical theory of concepts and still has effects today. For example, it has left its mark in the German standards DIN 2:)30 and DIN 2;3:)1. In mathematics it played a special role during the emergence of mathematical logic in the 19th century. Subsequently, however, it had virtually no impact on mathematical thinking. It was not until 1979 that the topic was revisited and treated more thoroughly. Since then, through a large number of contributions, Formal Concept Analysis has obtained such breadth that a systematic presentation is urgently needed, but can no longer be realized in one volume. Therefore, the present book foruse:':! on the mathematical foundations of Formal Concept Analysis, which ran be regarded chiefly as a branch of ap plied lattice theory. A series of examples serves to demonstrate the utility of the lnathematical definitions and results; in particular, to show how Formal Concept Analysis can be used for the conceptual unfolding of data contexts. These examples do not play the role of case studies in data analysis. A is intended for a comprehensive treatment of methods of separate volume conceptual data and knowledge processing. The general foundations of For mal Concept Analysis will also be treated separately.