A multi-color study of the variability of the magnetic cataclysmic variable BY Cam is presented. The observations were obtained at the Korean 1.8 m and Ukrainian 2.6 m, 1.2 m and 38 cm telescopes in 2003–2005, 56 observational runs cover 189 hours. The variations of the mean brightness in different colors are correlated with a slope dR/dV = 1:29(4), where the number in brackets denotes the error estimates in the last digits. For individual runs, this slope is much smaller ranging from 0.98(3) to 1.24(3), with a mean value of 1.11(1). Near the maximum, the slope becomes smaller for some nights, indicating more “blue” spectral energy distribution, whereas the night-to-night variability has an “infrared” character. For the simultaneous UBVRI photometry, the slopes increase with wavelength from dU/dR = 0:23(1) to dI/dR = 1:18(1). Such wavelength dependence is the opposite of that observed in non-magnetic cataclysmic variables, in agreement with the model of cyclotron emission. The principal component analysis shows two components of variablitity with different spectral energy distributions (with a third at the limit of detection), which possibly correspond to different regions of emission. The highest peak in the scalegram analysis corresponds to the 200 min spin variability, its quarter and to the 30 min and 8 min QPOs. The amplitudes of these components are dependent on wavelength and luminosity state. The light curves were fitted by a statistically optimal trigonometrical polynomial (up to 4th order) to take into account a 4-hump structure. The dependences of these parameters on the phase of the beat period and on mean brightness are discussed. The amplitude of spin variations increases with an increasing wavelength and with decreasing brightness. The linear ephemeris based on 46 mean minima for 2003–2005 is HJD 2453213:010(3) + 0:137123(3)E: The extensive tables of the original observations and of results of analysis are published in an electronic form. The nearby star GSC 4081–1562 was found to be an eclipsing red variable.