Algebraic curves are mathematical objects defined by polynomial equations in two variables, typically represented as x and y. These curves can take various shapes, such as lines, circles, and more complex forms, depending on the degree of the polynomial. For example, a simple linear equation like y = mx + b describes a straight line, while a quadratic equation like y = ax^2 + bx + c describes a parabola. These curves are studied in the field of algebraic geometry, which explores their properties and relationships. Algebraic curves can be classified based on their genus, which indicates the number of "holes" in the curve. Understanding these curves has applications in areas such as cryptography and computer graphics.