Diophantine approximation is a branch of Number Theory that can be described as the study of the solvability of inequalities in integers, though this main theme of the subject is often substantially generalized. As an example, one can be interested in properties of rational points of algebraic varieties defined over an algebraic number field, or as another example, one may study convergence rates of orbits for arithmetic dynamical systems. The proposed workshop is concerned with a variety of problems of this kind, which have seen important progress during the last few years. A detailed description is given below, where five (not unrelated) topics are emphasized. Among the new developments, let us mention works on the ZilberPink conjecture and on unlikely intersections; important progress in metric number theory; and progress towards the Uniform Boundedness Conjecture in dynamical systems.