Proteins perform a large variety of functions in living organisms and thus playa key role in biology. However, commonly used algorithms in protein learningwere not specifically designed for protein data, and are therefore not able tocapture all relevant structural levels of a protein during learning. To fill this gap,we propose two new learning operators, specifically designed to process proteinstructures. First, we introduce a novel convolution operator that considers theprimary, secondary, and tertiary structure of a protein by usingn-D convolutionsdefined on both the Euclidean distance, as well as multiple geodesic distancesbetween the atoms in a multi-graph. Second, we introduce a set of hierarchicalpooling operators that enable multi-scale protein analysis. We further evaluate theaccuracy of our algorithms on common downstream tasks, where we outperformstate-of-the-art protein learning algorithms.