The Pan-STARRS1 (PS1) $3pi$ survey is a comprehensive optical imaging survey of three quarters of the sky in the $grizy$ broad-band photometric filters. We present the methodology used in assembling the source classification and photometric redshift (photo-z) catalogue for PS1 $3pi$ Data Release 1, titled Pan-STARRS1 Source Types and Redshifts with Machine learning (PS1-STRM). For both main data products, we use neural network architectures, trained on a compilation of public spectroscopic measurements that has been cross-matched with PS1 sources. We quantify the parameter space coverage of our training data set, and flag extrapolation using self-organizing maps. We perform a Monte-Carlo sampling of the photometry to estimate photo-z uncertainty. The final catalogue contains $2,902,054,648$ objects. On our validation data set, for non-extrapolated sources, we achieve an overall classification accuracy of $98.1%$ for galaxies, $97.8%$ for stars, and $96.6%$ for quasars. Regarding the galaxy photo-z estimation, we attain an overall bias of $left<Delta z_{mathrm{norm}}right>=0.0005$, a standard deviation of $sigma(Delta z_{mathrm{norm}})=0.0322$, a median absolute deviation of $mathrm{MAD}(Delta z_{mathrm{norm}})=0.0161$, and an outlier fraction of $O=1.89%$. The catalogue will be made available as a high-level science product via the Mikulski Archive for Space Telescopes at https://doi.org/10.17909//t9-rnk7-gr88.
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