The paper presents nine new tunes of the $p_{\pm}$-ordered shower and underlying-event model in PYTHIA 6.4, referred to as the "Perugia" tunes, which update and replace the older "S0" family. These tunes are constrained by a variety of data sets, including hadronic $Z^{0}$ decays at LEP, Tevatron min-bias data at various energies, Tevatron Drell-Yan data, and SPS min-bias data. The Perugia tunes include a central parameter set called "Perugia 0" and eight related "Perugia variations" that explore systematic variations in theoretical parameters. The tunes are designed to provide a best-guess prediction of charged track multiplicity in inelastic, non-diffractive minimum-bias events at the LHC. The Perugia tunes are not compatible with PYTHIA 8 due to differences in parton-shower and color-reconnection models. The paper also discusses the tuning procedure, the main features of the Perugia tunes, and their extrapolation to the LHC. The tuning process involves five steps: final-state radiation and hadronization, initial-state radiation and primordial $k_T$, underlying event, beam remnants, and color reconnections, and energy scaling. The Perugia tunes aim to improve the description of jet shapes, strangeness yields, and high-$z$ fragmentation compared to the older tunes. The paper highlights the importance of jet universality and the need for independent tests of fragmentation models at hadron colliders.The paper presents nine new tunes of the $p_{\pm}$-ordered shower and underlying-event model in PYTHIA 6.4, referred to as the "Perugia" tunes, which update and replace the older "S0" family. These tunes are constrained by a variety of data sets, including hadronic $Z^{0}$ decays at LEP, Tevatron min-bias data at various energies, Tevatron Drell-Yan data, and SPS min-bias data. The Perugia tunes include a central parameter set called "Perugia 0" and eight related "Perugia variations" that explore systematic variations in theoretical parameters. The tunes are designed to provide a best-guess prediction of charged track multiplicity in inelastic, non-diffractive minimum-bias events at the LHC. The Perugia tunes are not compatible with PYTHIA 8 due to differences in parton-shower and color-reconnection models. The paper also discusses the tuning procedure, the main features of the Perugia tunes, and their extrapolation to the LHC. The tuning process involves five steps: final-state radiation and hadronization, initial-state radiation and primordial $k_T$, underlying event, beam remnants, and color reconnections, and energy scaling. The Perugia tunes aim to improve the description of jet shapes, strangeness yields, and high-$z$ fragmentation compared to the older tunes. The paper highlights the importance of jet universality and the need for independent tests of fragmentation models at hadron colliders.