Lévy processes with infinite jump activity present intricate stochastic dynamics. In this work, we focus on the non-parametric estimation of the increment density for both the entire process and the small-jump component. We develop spectral estimators, establish their convergence rates, and achieve minimax optimality.  This study is conducted under various observation regimes, including low- and high-frequency observations and with or without a Brownian component. Additionally, we construct adaptive estimators and assess their performance through numerical studies on α-stable and tempered stable Lévy processes. Our results enhance statistical inference techniques for stochastic models driven by jump processes.