We introduce Music Source Restoration (MSR), a novel task addressing the gap between idealized source separation and real-world music production. Current Music Source Separation (MSS) approaches assume mixtures are simple sums of sources, ignoring signal degradations employed during music production like equalization, compression, and reverb. MSR models mixtures as degraded sums of individually degraded sources, with the goal of recovering original, undegraded signals. Due to the lack of data for MSR, we present RawStems, a dataset annotation of 578 songs with unprocessed source signals organized into 8 primary and 17 secondary instrument groups, totaling 354.13 hours. To the best of our knowledge, RawStems is the first dataset that contains unprocessed music stems with hierarchical categories. We consider spectral filtering, dynamic range compression, harmonic distortion, reverb and lossy codec as possible degradations, and establish U-Former as a baseline method, demonstrating the feasibility of MSR on our dataset. We release the RawStems dataset annotations, degradation simulation pipeline, training code and pre-trained models to be publicly available.