Knowledge discovery in large and complex datasets is one main topic addressed by ``Data Science'' and is also a topic of first interest in ``Science of Knowledge'' (or Artificial Intelligence). Indeed data and knowledge are interacting: knowledge discovery is applied to datasets and has a direct impact on the design of knowledge bases (or ontologies). Accordingly, it could be interesting to have at hand a generic formalism supporting knowledge discovery and, as well, knowledge processing (knowledge representation and reasoning). In this presentation, we introduce some elements of Formal Concept Analysis (FCA), a mathematical formalism for data and knowledge processing. FCA starts with a binary table composed of objects and attributes and outputs a concept lattice. In a concept lattice, each concept is made of an intent (i.e. the description of the concept in terms of attributes) and an extent (i.e. the objects instances of the concept). Intents and extents are two dual facets of a concept that naturally apply in knowledge representation. Moreover, in some cases, the structure of a concept lattice can be visualized and allows a suggestive interpretation for human agents while being also processable by software agents. There are two main extensions of FCA, Relational Concept Analysis (RCA) for dealing with relational data and Pattern Structures (PS) for dealing with complex data (numbers, sequences, trees, graphs). We will discuss the capabilities of FCA and its extensions in knowledge discovery and knowledge engineering through various applications, including text mining, information retrieval, biclustering, recommendation, definition mining and discovery of functional dependencies.