In this course, Mathematics will be introduced from two points of view: Mathematics as a natural tool in Science, and Mathematics in the context of Number Theory. The first part of the course will present Mathematics as a necessary tool in the formalism of any scientific approach. In the second part, basic concepts of Classical Mechanics  necessary for the understanding of nature will be introduced as an application of the first part. In the third part, fundamental concepts in Number Theory -from ancient maths to most challenging problems not yet resolved -will be addressed in order to put the student in contact with the abstraction of pure Mathematics.