  The Heisenberg-Euler Lagrangian is not only a topic of fundamental interest,
but also has a rich variety of diverse applications in astrophysics, nonlinear
optics and elementary particle physics etc. We discuss the series
representation of this Lagrangian and a few of its applications in this study.
[In an appendix, we discuss issues related to the renormalization - and the
renormalization-group invariance - of the Heisenberg-Euler Lagrangian and its
two-loop generalization.]
