Neutrinos are elusive particles interacting weekly with the atomic nuclei and electron plasma. Most of the atomic nuclei that are stable from the strong interaction point of view can decay emitting neutrinos or antineutrinos. The properties of weak interaction are essential for the understanding of the fundamental symmetries that constrain the Standard Model of particle physics. Neutrinoless double beta decay, if observed, would signal physics beyond the Standard Model (BSM). We analyze the neutrino physics relevant for the double beta decay of the atomic nuclei. Contributions to the decay rate from different terms in the BSM Lagrangian are presented, and their relevance for the analysis of the experimental data are addressed. We investigate if the neutrino mixing effects in the high electron density inside the atomic nuclei can change the neutrinoless double beta decay half-life formula and we found that the standard result stands.