While silicon (Si) has tenfold capacity of commercially used graphite, its application is still limited due to its limited cyclability. In this in situ X-ray reflectivity study, a detailed mechanistic model of the first two (de)lithiation processes of a silicon wafer is presented, which sheds light onto the fundamental difference of the reaction of Li ions with crystalline and amorphous materials. Furthermore, this study provides insight into the formation and further evolution of the inorganic solid electrolyte interphase (SEI) layer on Si anodes. The results show that the lithiation of crystalline Si is a layer-by-layer, reaction limited two-phase process, but the delithiation of LixSi (resulting in amorphous Si) and the lithiation of amorphous Si are reaction-limited single-phase processes. Furthermore, the thickness-density product of the inorganic SEI layer increases during lithiation and decreases during delithiation, resembling a breathing behavior; the inorganic SEI layer thickness varies between 40 and 70 angstrom. Additionally, a low-electron-density Li-dip layer is found between the SEI and lithiated Si during the delithiation process, suggesting kinetically limited ion transport within the SEI, which is speculated to be one of the origins of battery's internal resistance. Several implications of the findings on battery performance in general are discussed.