This course aims to provide an introduction to the fundamental concepts in the area of argumentation mining. This is an area with strong background in linguistics and in artificial intelligence, with clearly applied goals. In this course we aim to provide students with an insight of the phenomena that are found in argumentative texts and dialogues, their complexity and their characteristics. Then, we describe different approaches to formalizing these phenomena and the argumentation process in general. Finally, we present different applications of argumentation mining, in the domains of legal texts, debating or mining scientific literature, and we show different approaches to bridge the gap between theory and application. We devote a special emphasis to the manual annotation of argumentative texts for different purposes, for students to narrow down abstract concepts and to better understand the idiosyncrasy of argumentative phenomena, all of this with applied goals in sight.