To the students interested in attending the course, this is a basic description of the program. The first part of the course provides an introduction to commutative algebra, covering topics such as localization, spectrum of a ring and Noetherian property. The second part builds upon the first in order to study fundamental results about algebraic varieties over algebraically closed fields. The course will finish with some applications to cryptography. More precisely, regarding how the elliptic curve discrete logarithm problem provides examples for key agreement and digital signatures that are currently being used in cryptography. For additional information you can write to Prof. Lleonard Rubio y Degrassi, lleonard.rubioydegrassi@univr.it