We present calculated valence and C 1s near-edge excitation spectra of solid C60 and experimental results measured with high-resolution electron energy-loss spectroscopy. The near-edge calculations are carried out using three different methods: solution of the Bethe-Salpeter equation (BSE) as implemented in the OCEAN suite (Obtaining Core Excitations with ab initio methods and the NIST BSE solver), the excited-electron core-hole approach (XCH), and the constrained-occupancy method using the Stockholm-Berlin core-excitation code, StoBe. The three methods give similar results and are in good agreement with experiment, though the BSE results are the most accurate. The BSE formalism is also used to carry out valence level calculations using the NIST Bethe-Salpeter Equation solver (NBSE). Theoretical results include self-energy corrections to the band gap and band widths, lifetime-damping effects, and Debye-Waller effects in the core-excitation case. A comparison of spectral features to those observed experimentally illustrates the sensitivity of certain features to computational details, such as self-energy corrections to the band structure and core-hole screening.