We study the magnetic fields of the Serpens Main molecular cloud consisting of two subclusters and six filamentary structures, as part of the B-fields in Star-forming Region Observations (BISTRO) survey that is a large program using the James Clerk Maxwell Telescope (JCMT) to study the roles of magnetic fields in molecular clouds on intermediate scales (a few thousands au or larger scales). Using the Histogram of Relative Orientation (HRO) technique, which compares polarization directions with density gradients, we find that magnetic fields are parallel to filaments in less dense regions, N(H_2) < ~10^22 /cm^2, but perpendicular to dense filamentary structures. Furthermore, applying the HRO technique to denser core regions we identify the density regimes in which the relative magnetic field orientations change again. These transitions are understood to happen where core formation occurs (N(H_2) ? 4.6 × 10^22 /cm^2) and where magnetic fields are dragged-in by infalling material (N(H_2) ? 16 × 10^22 /cm^2). In addition, the magnetic field strengths in filamentary structures are estimated by the Davis-Chandrasekhar-Fermi method and compared with turbulence and gravity.