  We present a straightforward and self-contained introduction to the basics of
the loop approach to quantum gravity, and a derivation of what is arguably its
key result, namely the spectral analysis of the area operator. We also discuss
the arguments supporting the physical prediction following this result: that
physical geometrical quantities are quantized in a non-trivial, computable,
fashion. These results are not new; we present them here in a simple form that
avoids the many non-essential complications of the first derivations.
