  In this paper, we analyze multi-dimensional $({\mathrm R}_{X},{\mathcal
B})$-almost periodic type functions and multi-dimensional Bohr ${\mathcal
B}$-almost periodic type functions. The main structural characterizations and
composition principles for the introduced classes of almost periodic functions
are established. Several applications of our abstract theoretical results to
the abstract Volterra integro-differential equations in Banach spaces are
provided, as well.
