This research school will introduce the participants to some basics of algebraic geometry with an emphasis on computational aspects, such as Groebner bases and combinatorial aspects, such as toric varieties and tropical geometry. We will also learn how to use the freely available software Macaulay2 for studying algebraic varieties. The lecturers for this school are all active in these areas and collectively have deep experience both as researchers and educators through the supervision of students ; Ph.D. and postdoctoral, as well as the organization of and lecturing in short courses.