This subject develops abstract algebraic thought to a higher level. The abstract concepts introduced in the subject, ring theory, field theory and algebraic equations, have many applications in science and technology. The theory of algebraic equations is the study of solutions of polynomial equations. Although the problem originates in explicit manipulations of polynomials, the modern (and far more powerful) treatment is in terms of field extensions. The subject is an introduction to ring theory and field theory; it includes applications to cryptography (RSA) and geometry (proving that it is impossible to trisect an arbitrary angle using only a straightedge and compass).