An abelian differential defines a Euclidean metric with conical singularities such that the underlying Riemann surface can be realized as a polygon with edges pairwise identified via translation. Varying the shape of such polygons induces a GL(2,R)-action on the moduli space of abelian differentials, called Teichmueller dynamics, whose study has provided fascinating results in many fields, including (but not limited to) the works of a number of Fields Medalists (Avila, Kontsevich, McMullen, Mirzakhani, Okounkov, Yoccoz, etc). In this lecture series I will give an elementary introduction to this beautiful subject, with a focus on a combination of analytic, algebraic, dynamical, and combinatorial viewpoints.