We investigate how the Large Magellanic Cloud (LMC) influences the evolution of the Galaxy after the LMC enters the virial radius of the dark matter halo of the Galaxy for the first time. Both the Galaxy and the LMC are modelled as N-body particles in our models so that the dynamical influences of the LMC on the Galaxy can be investigated in a fully self-consistent manner. Furthermore, the orbital parameters for the LMC are carefully chosen such that the present location of the LMC in the Galaxy can be rather precisely reproduced in our simulations. We particularly investigate the influences of the LMC on the precession rate, the outer stellar and gaseous structures, and the star formation history of the Galaxy. Our principal results are summarized as follows. The LMC–Galaxy dynamical interaction can cause ‘pole shift’ (or irregular precession/nutation) of the Galaxy and the typical rate of pole shift () is ∼2° Gyr−1 corresponding to as yr−1. The LMC–Galaxy interaction induces the formation of the outer warp structures of the Galaxy, which thus confirms the results of previous numerical simulations on the formation of the Galactic warp. The LMC–Galaxy interaction also induces the formation of outer (R > 20 kpc) spiral arms and increases the vertical velocity dispersion of the outer disc significantly. The mean star formation rate of the Galaxy for the last several Gyr can be hardly influenced by the LMC’s tidal force. The age and metallicity distribution of stars in the solar neighbourhood (7 ≤R≤ 10 kpc) for the last several Gyr can be only slightly changed by the past LMC–Galaxy interaction. If the LMC is accreted on to the Galaxy as a group with small dwarf galaxies, then the stripped dwarfs form a unique polar distribution within the Galaxy. Based on these results, we discuss how the possible ongoing Galactic pole shift with as yr−1 can be detected by future observational studies by Gaia.