Invariant theory is the study of invariants of homogeneous polynomials. Perhaps the best known example of an invariant is the discriminant b^2 - 4ac of a quadratic polynomial. In this thesis, we...Show moreInvariant theory is the study of invariants of homogeneous polynomials. Perhaps the best known example of an invariant is the discriminant b^2 - 4ac of a quadratic polynomial. In this thesis, we will consider invariants of binary quintics, which are homogeneous polynomials in two variables of degree five. Given values for the invariants, we (re)construct a binary quintic that attains this tuple of values. We will also discuss the implementation of these methods in SageMath, a free open-source mathematics software system.Show less