This first lecture will concentrate on double Schubert polynomials, as preparation for the back-stable generalizations which will be the main focus of the series. We will describe some of the history - emphasizing discoveries where back-stable ideas can be seen (with hindsight). In addition to their algebraic formulas, we will discuss how they are characterized geometrically by giving formulas for degeneracy loci (putting rank conditions on matrices), and we will describe Lam, Lee and Shimozono's combinatorial formula for them in terms of bumpless pipe dreams.