  We use basic physics and simple mathematics accessible to advanced
undergraduate students to estimate the main properties of neutron stars. We set
the stage and introduce relevant concepts by discussing the properties of
"everyday" matter on Earth, degenerate Fermi gases, white dwarfs, and scaling
relations of stellar properties with polytropic equations of state. Then, we
discuss various physical ingredients relevant for neutron stars and how they
can be combined in order to obtain a couple of different simple estimates of
their maximum mass, beyond which they would collapse, turning into black holes.
Finally, we use the basic structural parameters of neutron stars to briefly
discuss their rotational and electromagnetic properties.
