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We report normalized experimental and theoretical differential cross sections for elastic electron scattering by ${\mathrm{C}}_{4}$H${}_{4}$O (furan) molecules from a collaborative project between several Brazilian theoretical groups and an experimental group at California State Fullerton, USA. The measurements are obtained by using the relative flow method with helium as the standard gas and a thin aperture target gas collimating source. The relative flow method is applied without the restriction imposed by the relative flow pressure condition on helium and the unknown gas. The experimental data were taken at incident electron energies of 1, 1.5, 1.73, 2, 2.7, 3, 5, 7, 10, 20, 30, and 50 eV and covered the angular range between ${10}^{\ifmmode^\circ\else\textdegree\fi{}}$ and ${130}^{\ifmmode^\circ\else\textdegree\fi{}}$. The measurements verify observed ${\ensuremath{\pi}}^{*}$ shape resonances at $1.65\ifmmode\pm\else\textpm\fi{}0.05$eV and $3.10\ifmmode\pm\else\textpm\fi{}0.05$ eV scattering energies, in good agreement with the transmission electron data of Modelli and Burrow [J. Phys. Chem. A 108, 5721 (2004)]. Furthermore, the present results also indicated both resonances dominantly in the $d$-wave channel. The differential cross sections are integrated in the standard way to obtain integral elastic cross sections and momentum transfer cross sections. The calculations employed the Schwinger multichannel method with pseudopotentials and were performed in the static-exchange and in the static-exchange plus polarization approximations. The calculated integral and momentum transfer cross sections clearly revealed the presence of two shape resonances located at 1.95 and 3.56 eV and ascribed to the ${B}_{1}$ and ${A}_{2}$ symmetries of the ${C}_{2v}$ point group, respectively, in very good agreement with the experimental findings. Overall agreement between theory and experiment regarding the differential, momentum transfer, and integral cross sections is very good, especially for energies below 10 eV.