  We theoretically investigate multiple-$Q$ spin textures, which are composed
of superpositions of spin density waves with different wave numbers, for an
effective spin model of centrosymmetric itinerant magnets. Our focus is on the
interplay between biquadratic interactions arising from the spin-charge
coupling and magnetic anisotropy caused by the spin-orbit coupling. Taking into
account two types of the magnetic anisotropy, single-ion anisotropy and
bond-dependent anisotropy, we elucidate magnetic phase diagrams for an
archetypal triangular-lattice system in the absence and presence of an external
magnetic field. In the case of the single-ion anisotropy, we find a plethora of
multiple-$Q$ instabilities depending on the strength and the sign of the
anisotropy (easy plane or easy axis), including a skyrmion crystal with
topological number of two. In an external magnetic field, we find that a
skyrmion crystal with topological number of one is stabilized by the in-plane
(out-of-plane) magnetic field under the easy-plane (easy-axis) anisotropy. We
also examine the stability of the field-induced skyrmion crystal by rotating
the field direction. As a biproduct, we show that a triple-$Q$ state with
nonzero chirality appears in the presence of the biquadratic interaction and
the easy-axis anisotropy. Meanwhile, we find that the bond-dependent anisotropy
also stabilizes both types of skyrmion crystals. We show that, however, for the
skyrmion crystal with topological number of one, Bloch- and N\'eel-type
skyrmion crystals are selectively realized depending on the sign of the
bond-dependent anisotropy. Moreover, we find yet another multiple-$Q$ states,
including two types of meron crystals with the skyrmion numbers of one and two.
The systematic investigation will provide a reference to complex magnetic
textures in centrosymmetric magnetic metals.
