The main target of this course is introducing the student to some themes in the philosophical literature about the sorites paradox and the Liar paradox as well as to some logical developments connected to them. More specifically, with this course we expect the students to reach the following goals: (i) knowing the philosophical significance of the sorites paradox and of the Liar paradox, (ii) knowing some basic reactions to the sorites paradox and to the Liar paradox. (iii) acquiring familiarity with the logics K3, LP and ST. (iv) mastering the concepts of paracompleteness, paraconsistency and duality. (v) acquiring familiarity with the use of multiple conclusions. (vi) mastering the tableaux technique to construct proofs for classical propositional logic, K3, LP, ST.