Algebraic geometry is a branch of mathematics that studies the solutions of systems of polynomial equations. It combines concepts from algebra and geometry to explore the properties of shapes and spaces defined by these equations. This field helps mathematicians understand the relationships between algebraic expressions and geometric structures. In algebraic geometry, objects called varieties are central. Varieties can be thought of as the geometric manifestations of polynomial equations. By analyzing these varieties, mathematicians can uncover important information about their dimensions, intersections, and other characteristics, leading to insights in both pure and applied mathematics.