Algebraic geometry is a classical and nowadays vast area of mathematics. It deals with geometric figures given as roots of polynomial equations. Such figures live in projective spaces and are called algebraic varieties. Algebraic geometry marvellously merges different kinds of geometry and number theory into one big field. In the last decades the role of algebraic geometry in theoretical physics is steadily increasing. Within this advanced and demanding one-semester module the students will learn basics of algebraic geometry, being concentrated on the detailed elaboration of some instructive examples illustrating fundamental concepts and phenomena. Our purpose would be to train our algebraic-geometrical intuition working both synthetically, i.e. without coordinates, and in coordinates in terms of polynomials with coefficients in an algebraically closed field.