The 13th International Conference on “Concept Lattices and Applications (CLA 2016)” was held at National Research University Higher School of Economics, Moscow, Russia from July 18 until July 22, 2016. The CLA conference, organized since 2002, aims to provide to everyone interested in Formal Concept Analysis and more generally in Concept Lattices or Galois Lattices, an advanced view on some of the last research trends and applications in this field. It also aims to bring together students, professors, researchers and engineers, involved in all aspects of the study of concept lattices, from theory to implementations and practical applications. As the diversity of the selected papers shows, there is a wide range of research directions, around data and knowledge processing, including data mining, knowledge discovery, knowledge representation, reasoning, pattern recognition, together with logic, algebra and lattice theory. The program of the conference includes four keynote talks given by the following distinguished researchers: Lev D. Beklemishev (Mathematical Institute of Russian Academy of Science, Moscow), J´erˆome Euzenat (INRIA Grenoble Rhˆone-Alpes), Bernhard Ganter (TU-Dresden), Boris G. Mirkin (National Research University Higher School of Economics, Moscow). This volume includes the selected papers and the abstracts of the invited talks. This year, 46 papers were submitted, from which 28 papers were accepted as regular papers. We would like to thank here the contributing authors for their valuable work, the members of the program committee and the external reviewers who analyzed the papers with care. All of them participated to the continuing quality and importance of CLA, highlighting its key role in the field. Then we would also like to thank the steering committee of CLA for giving us the occasion of leading this edition of CLA, the conference participants for their participation and support, and people in charge of the organization, especially Larisa I. Antropova, Ekaterina L. Chernyak, Dmitry I. Ignatov, Olga V. Maksimenkova, whose help was very precious in many occasions and that contributed to the success of the event. We would like to thank our sponsors, namely National Research University Higher School of Economics, ExactPro company, Russian Foundation for Basic Research. Finally, we also do not forget that the conference was managed (quite easily) with the Easychair system, for many tasks including paper submission, selection, and reviewing.