Algebraic Geometry. Start Up Course

Algebraic geometry studies geometric loci looking locally as a solution set for a system of polynomial equations on an affine space. It gives an explicit algebraic explanation for various geometric properties of figures, and in the same time, brings up a geometric intuition underlying abstract purely algebraic constructions. It plays an important role in many areas of mathematics and theoretical physics, and provides the most visual and elegant tools to express all aspects of the interaction between different branches of mathematical knowledge. The course gives the geometric flavor of the subject by presenting examples and applications of the ideas of algebraic geometry, as well as a first discussion of its technical tools.