The results of studies of an electrical breakdown leading to the glow discharge ignition in a long capillary quartz tube are presented. Under such conditions, the breakdown completion is preceded by the development of direct, backward, and counter slow ionization waves (IWs) traveling in the tube. The initiation of the waves was created in helium at low pressure (P = 10 Torr) by the high-voltage pulses of positive and negative polarity with amplitude of several kilovolts. In the beginning, the regime without the breakdown completion in the tube was studied. In this regime, the propagation of only direct positive and direct negative IWs happens. The research on dynamics of the direct, backward, and counter positive and negative waves followed by a complete breakdown was done as well. The influence of the pre-existing plasma on the IWs propagation was also studied. The plasma was created in advance by low-current glow discharge being formed in the tube. The instant images of IWs were correlated with the electrical currents formed by the waves, that is, with the displacement current through the dielectric wall and the conductive current through the plasma column. In the experiments, the fine-sectioned electrode wrapped around the lateral tube surface was used. The usage of such electrode allowed one to study the dynamics of the surface charge deposition and deletion happening during the direct and backward wave propagation, respectively. Finally, a strong difference in the spatial structure and velocity of positive and negative direct waves traveling through non-ionized gas was revealed. Contrary, both the positive and negative backward waves traveling through the plasma formed by previous direct waves have the parameters close to each other.