In this tutorial we will introduce and discuss how FCA and two main extensions, namely Pattern Structures and Relational Concept Analysis (RCA), can be used for knowledge discovery purposes, especially in pattern and rule mining, in data and knowledge processing, data analysis, and classification. Indeed, FCA is aimed at building a concept lattice starting from a binary table where objects are in rows and attributes in columns. But FCA can deal with more complex data. Pattern Structures allow to consider objects with descriptions based on numbers, intervals, sequences, trees and general graphs. RCA was introduced for taking into account relational data and especially relations between objects. These two extensions rely on adapted FCA algorithms and can be efficiently used in real-world applications for knowledge discovery, e.g. text mining and ontology engineering, information retrieval and recommendation, analysis of sequences based on stability, semantic web and classification of Linked Open Data, biclustering, and functional dependencies.