In this thesis, we present our result on the theory of pre-orthogonal adaptive Fourier decomposition (POAFD) and its weakened variant weak pre-orthogonal adaptive Fourier decomposition (WPOAFD) of functions in Bergman spaces on some classes of higher-dimensional complex bounded domains in Cᴺ. In [27, 28, 29, 31], Prof. Qian and his collaborators developed the pre-orthogonal adaptive Fourier decomposition of functions in the Bergman space A²(D) on the unit disk D, among other things. They showed that the Bergman space A²(D) satisfies the boundary vanishing property (BVP). By BVP and introducing generalized kernel functions, they also showed that the maximal selection principle holds so that any given function in A²(D) can be expanded with an orthonormal system constructed from reproducing kernel functions in a sense of greedy algorithm in L² norm. Inspired by these ideas, we generalize the POAFD scheme from the case of Bergman space A²(D) to the case of Bergman space A²(D) on any irreducible bounded symmetric domain D of type I. We show that A²(D) satisfies the boundary vanishing property, so that the maximal selection principle allows us to give an adaptive expansion of any function f ∈ A²(D) in terms of linear combinations of generalized kernel functions in a sense of greedy algorithm. In order to show that maximal selection principle holds in the higher dimensional case, the estimates of decomposition of functions involving generalized kernel functions are more much technical than that in the one-dimensional case. We also study the WPOAFD for Bergman space on any irreducible bounded symmetric domain of type I, II, III, IV and Bergman space on any bounded (strictly) pseudoconvex domain with smooth boundary. In these cases, we show that weak maximal selection principle holds, which implies that any function in these Bergman spaces can be approximated by linear combinations of kernel functions in a weak greedy sense. In the WPOAFD scheme, where generalized kernel functions are not involved, we expect that computational complexity in WPOAFD scheme is much lower than that in POAFD scheme.