  We explore, at T=0, the magnetic properties of the $S=1/2$ antiferromagnetic
distorted diamond chain described by the Hamiltonian ${\cal H}
  = \sum_{j=1}^{N/3}{J_1 ({\bi S}_{3j-1} \cdot {\bi S}_{3j}
  + {\bi S}_{3j} \cdot {\bi S}_{3j+1})
  + J_2 {\bi S}_{3j+1} \cdot {\bi S}_{3j+2}
  + J_3 ({\bi S}_{3j-2} \cdot {\bi S}_{3j}
  + {\bi S}_{3j} \cdot {\bi S}_{3j+2})}
  \allowbreak - H \sum_{l=1}^{N} S_l^z $ with $J_1, J_2, J_3\ge0$, which well
models ${\rm A_3 Cu_3 (PO_4)_4}$ with ${\rm A = Ca, Sr}$, ${\rm Bi_4 Cu_3 V_2
O_{14}}$ and azurite $\rm Cu_3(OH)_2(CO_3)_2$. We employ the physical
consideration, the degenerate perturbation theory, the level spectroscopy
analysis of the numerical diagonalization data obtained by the Lanczos method
and also the density matrix renormalization group (DMRG) method. We investigate
the mechanisms of the magnetization plateaux at $M=M_s/3$ and $M=(2/3)M_s$, and
also show the precise phase diagrams on the $(J_2/J_1, J_3/J_1)$ plane
concerning with these magnetization plateaux, where $M=\sum_{l=1}^{N} S_l^z$
and $M_s$ is the saturation magnetization. We also calculate the magnetization
curves and the magnetization phase diagrams by means of the DMRG method.
