Solar storms, accompanied by flares, coronal mass ejections, and the generation of high-speed solar wind streams, cause a set of physical processes in the geospace environment and on Earth. The collective manifestation of these processes is referred to as a geospace storm. Geospace storms are associated with intense disturbances of the geomagnetic field, the ionosphere, the upper atmosphere (thermosphere), the geoelectric field of magnetospheric-ionospheric-atmospheric origin, the troposphere, and telluric currents. All these disturbances are closely interconnected. Therefore, a geospace storm can be understood as a synergistically interacting system of magnetic, ionospheric, atmospheric, and electrical storms. Every geospace storm is a unique phenomenon. In addition to general patterns, each storm has its own individual characteristics. For this reason, the study of each new storm remains a relevant scientific task. An interesting event occurred in early January 2015, a recurrent sequence of three geomagnetic storms over the course of one week. The purpose of this study is to describe the features of fluctuations in the level and spectral composition of the geomagnetic field during these three successive storms from January 2 to 8, 2015. The core of the magnetometric system located at the magnetometric observatory of the V. N. Karazin Kharkiv National University (geographic coordinates: 49.65°N, 36.93°E) is the IM-II induction magnetometer-fluxmeter. It offers high sensitivity (0.5...500 pT for periods of 1...1000 s, respectively). The signal output from the magnetometer, initially in relative units and accounting for the instrument’s amplitude-frequency characteristics, is first converted into absolute units (in nanoteslas). Time series of the amplitudes of the horizontal components of the geomagnetic field are then constructed. Subsequently, a system spectral analysis is performed across the period range of 1...1000 s. Analysis of the three recurrent geospace and magnetic storms observed near the maximum of the 24th solar activity cycle revealed the following. During January 2/3, 4/5, and 7/8, 2015, severe magnetospheric storms occurred, with corresponding powers of 180, 240, and 530 GJ/s and energies of approximately 1920, 4800, and 10500 TJ, respectively. The magnetic storms during January 2/3, 4/5, and 7/8, 2015, were classified as rather moderate, moderate, and strong, with associated energies of 2.5, 3.1, and 4.9 PJ, and power P₁ of about 200, 50, and 600 GW. Simultaneously, the P₂ power reached 32, 12, and 23 GW, respectively. During January 2/3, 4/5, and 7/8, 2015, the fluctuation level of the horizontal components of the geomagnetic field increased from 0.5 nT by factors of approximately 4...5, 2...3, and 8...10, respectively. These increases correlated with the average power of the geomagnetic storm during its main phase. During the magnetic storms, fluctuations in the geomagnetic field were dominated by components with periods of 700...1000 s. Oscillations with periods of 140...200 s had slightly lower amplitudes, and those with periods of 40...50 s were the weakest. The three consecutive magnetic storms, occurring near the solar activity maximum, were classified as rather moderate, moderate, and strong.