We start with the Bruhat decomposition of the full flag variety and the Borel presentation of its cohomology ring to introduce the Schubert polynomials, the main objects of interest for this seminar. We will then briefly discuss several topics that can be covered throughout the semester, including various monomial expansions of the Schubert polynomials, combinatorial algebraic geometry of the Schubert varieties, Gröbner geometry of matrix Schubert varieties and more.