We propose experiments in the E7 and E4 experimental areas at ELI-NP to tackle problems of fundamental physics, taking advantage of the unique configuration and characteristics of the new research infrastructure to be constructed in Magurele, Romania. The experimental setups proposed follow a gradual approach from the point of view of complexity, from the "Day 1" experiments to experiments for which the prerequisites include results from the previously performed ones. In addition, there are two generic Research and Development tasks proposed in this Technical Design Report (TDR), related to the development of a detection system, Gamma Polari-Calorimeter (GPC), commonly applicable to energy measurements for electrons, positrons and gamma-rays above the 0.1 GeV energy scale and the preparatory tests for laser plasma acceleration of electrons up to necessary energies 210 MeV, 2.5 GeV and 5 GeV for the later stage experiments, respectively. In this paper we particularly focus on possible "Day-1" topics and briefly mention the future extensions foreseen.
