This free course contains an introduction to rings and polynomials. We see that polynomial rings have many properties in common with the integers; for example, we can define a division algorithm, and this enables us to develop the analogue of the highest common factor for two polynomials. Section 1 explores the abstract definitions of a ring and a field. Sections 2 and 3 define polynomial rings where the coefficients of the polynomials are elements from a given field. Section 3 develops results concerning the divisibility of polynomials.