The 26Al radioisotope is of great importance for understanding the chemical and dynamical evolution of our galaxy. Among the possible stellar sources, massive stars are believed to be the main producer of this radioisotope. Understanding 26Al nucleosynthesis in massive stars requires estimates of the thermonuclear reaction rates of the Al26(n,p)26Mg, Al26(n,α)23Na, and Na23(α,p)26Mg reactions. These reaction rates depend on the spectroscopic properties of 27Al states above the neutron and alpha thresholds. In this context, the Al27(p,p')27Al* reaction was studied at 18 MeV using a high-resolution Enge Split-Pole spectrometer. States from the ground state up to excitation energies of ≈14 MeV were populated. While up to the 23Na + α threshold no additional states are observed, we report for the first time 30 new levels above the 23Na + α threshold and more than 30 new states above the 26Al + n threshold for which excitation energies are determined with an uncertainty of 4-5 keV.