  We use the full-mission $\textit{Planck}$ PR4 data to construct maps of the
thermal Sunyaev$--$Zel'dovich effect (Compton-$y$ parameter) in our Universe.
To do so, we implement a custom needlet internal linear combination (NILC)
pipeline in a Python package, $\texttt{pyilc}$, which we make publicly
available. We publicly release our Compton-$y$ maps, which we construct using
various constrained ILC ("deprojection") options in order to minimize
contamination from the cosmic infrared background (CIB) in the reconstructed
signal. In particular, we use a moment-based deprojection which minimizes
sensitivity to the assumed frequency dependence of the CIB. Our code
$\texttt{pyilc}$ performs needlet or harmonic ILC on mm-wave sky maps in a
flexible manner, with options to deproject various components on all or some
scales. We validate our maps and compare them to the official $\textit{Planck}$
2015 $y$-map, finding that we obtain consistent results on large scales and
10-20$\%$ lower noise on small scales. We expect that these maps will be useful
for many auto- and cross-correlation analyses; in a companion paper, we use
them to measure the tSZ -- CMB lensing cross-correlation. We anticipate that
$\texttt{pyilc}$ will be useful both for data analysis and for pipeline
validation on simulations to understand the propagation of foreground
components through a full NILC pipeline.
