Algebraic surfaces are geometric objects defined by polynomial equations in three-dimensional space. They can be visualized as the set of points that satisfy a given equation, such as x² + y² + z² = 1, which describes a sphere. These surfaces are studied in the field of algebraic geometry, where mathematicians explore their properties and relationships. These surfaces can be classified into various types, such as smooth and singular surfaces, depending on their geometric features. Understanding algebraic surfaces helps in solving complex problems in mathematics and has applications in areas like computer graphics and theoretical physics.