The school aims to introduce graduate students and young researchers to key topics in algebraic number theory and arithmetic geometry as well as their computational aspects. Modular forms and elliptic curves will be central, with a view towards Galois representations, complex multiplication and class field theory. Understanding of the abstract theory will be facilitated by an explicit and algorithmic approach, through interactive activities where we will make use of freely available computer algebra systems. The participants will be provided with an introduction to the basic material before proceeding to the more advanced topics.