  The complex scaling method (CSM) is a useful similarity transformation of the
Schr\"odinger equation, in which bound-state spectra are not changed but
continuum spectra are separated into resonant and non-resonant continuum ones.
Because the asymptotic wave functions of the separated resonant states are
regularized by the CSM, many-body resonances can be obtained by solving an
eigenvalue problem with the $L^2$ basis functions. Applying this method to a
system consisting of a core and valence nucleons, we investigate many-body
resonant states in weakly bound nuclei very far from the stability lines.
Non-resonant continuum states are also obtained with the discretized
eigenvalues on the rotated branch cuts. Using these complex eigenvalues and
eigenstates in CSM, we construct the extended completeness relations and
Green's functions to calculate strength functions and breakup cross sections.
Various kinds of theoretical calculations and comparisons with experimental
data are presented.
