  The Pierre Auger Observatory is the world's largest detector for observation
of ultra-high-energy cosmic rays (UHECRs) (above the energy of $10^{17}$ eV).
It consists of a Fluorescence Detector (FD) and an array of particle detectors
known as the Surface Detector (SD). Observations of extensive air showers by
the Observatory can be used to probe hadronic interactions at high energy, in a
kinematic and energy region inaccessible to experiments at man-made
accelerators and to measure the muon component of the shower. Air showers
induced by different primaries have different muon contents. With increasing
mass of the primary cosmic ray particle, it is expected that the muon content
in the corresponding air showers should also increase. Recent results obtained
from the Pierre Auger Observatory and other experiments indicate that all the
shower simulations underestimate the number of muons in the showers compared to
the data. This is the so-called muon deficit. In this paper we briefly review
the muon measurements, and present in more detail recent results on
fluctuations in the muon number. These results provide new insights into the
origin of the muon deficit in air shower simulations and constrain the models
of hadronic interactions at ultrahigh energies. With the current design of the
surface detectors it is also difficult to reliably separate the contributions
of muons to the SD signal from the contributions of photons, electrons, and
positrons. Therefore, we also present a new method to extract the muon
component of the signal time traces recorded by each SD station using recurrent
neural networks. The combination of such algorithms, with the future data
collected by the upgraded Pierre Auger Observatory, will be a major step
forward, as we are likely to achieve an unprecedented resolution in mass
estimation on an event-by-event basis.
