Absorption lines of H$_2$ and HD molecules observed at high redshift in the line of sight towards quasars are a test ground to search for variation of the proton-to-electron mass ratio $mu$. For this purpose, results from astronomical observations are compared with a compilation of molecular data of the highest accuracy, obtained in laboratory studies as well as in first-principles calculations. Aims: A comprehensive line list is compiled for H$_2$ and HD absorption lines in the Lyman ($B^1Sigma_u^+$ - $X^1Sigma_g^+$) and Werner ($C^1Pi_u$ - $X^1Sigma_g^+$) band systems up to the Lyman cutoff at 912 Angstroms. Molecular parameters listed for each line $i$ are the transition wavelength $lambda_i$, the line oscillator strength $f_i$, the radiative damping parameter of the excited state $Gamma_i$, and the sensitivity coefficient $K_i$ for a variation of the proton-to-electron mass ratio. Methods: The transition wavelengths $lambda_i$ for the H$_2$ and HD molecules are determined by a variety of advanced high-precision spectroscopic experiments involving narrowband vacuum ultraviolet lasers, Fourier-transform spectrometers, and synchrotron radiation sources. Results for the line oscillator strengths $f_i$, damping parameters $Gamma_i$, and sensitivity coefficients $K_i$ are obtained in theoretical quantum chemical calculations. Results: A new list of molecular data is compiled for future analyses of cold clouds of hydrogen absorbers, specifically for studies of $mu$-variation from quasar data. The list is applied in a refit of quasar absorption spectra of B0642$-$5038 and J1237$+$0647 yielding constraints on a variation of the proton-to-electron mass ratio $Deltamu/mu$ consistent with previous analyses.
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