This volume contains the Proceedings of ICFCA 2004, the 2nd International Conference on Formal Concept Analysis. The ICFCA conference series aims to be the premier forum for the publication of advances in applied lattice and order theory and in particular scientific advances related to formal concept analysis. Formal concept analysis emerged in the 1980s from efforts to restructure lattice theory to promote better communication between lattice theorists and potential users of lattice theory.Since then, the fieldhasdevelopedintoagrowing research area in its own right with a thriving theoretical community and an increasing number of applications in data and knowledge processing including data visualization, information retrieval, machine learning, data analysis and knowledge management. In terms of theory, formal concept analysis has been extended into attribute exploration, Boolean judgment, contextual logic and so on to create a powerful general framework for knowledge representation and reasoning. This conference aims to unify theoretical and applied practitioners who use formal concept an- ysis, drawing on the fields of mathematics, computer and library sciences and software engineering. The theme of the 2004 conference was ‘Concept Lattices” to acknowledge the colloquial term used for the line diagrams that appear in almost every paper in this volume. ICFCA 2004 included tutorial sessions, demonstrating the practical benefits of formal concept analysis, and highlighted developments in the foundational theory and standards. The conference showcased the increasing variety of formal concept analysis software and included eight invited lectures from distinguished speakersinthe field. Seven of the eight invited speakers submitted accompanying papers and these were reviewed andappear in this volume.