  In the framework of the spectral integral equation, we consider the $b\bar b$
states and their radiative transitions. We reconstruct the $b\bar b$
interaction on the basis of data for the levels of the bottomonium states with
$J^{PC}=0^{-+}$, $1^{--}$, $0^{++}$, $1^{++}$, $2^{++}$ as well as the data for
the radiative transitions $\Upsilon(3S) \to\gamma\chi_{bJ}(2P) $ and
$\Upsilon(2S) \to\gamma \chi_{bJ}(1P) $ with $J=0,1,2$. We calculate
bottomonium levels with the radial quantum numbers $n\le 6$, their wave
functions and corresponding radiative transitions. The ratios
$Br[\chi_{bJ}(2P)\to\gamma\Upsilon(2S)]/Br[\chi_{bJ}(2P)\to\gamma\Upsilon(1S)]$
for $J=0,1,2$ are found in the agreement with data. We determine the $b\bar b$
component of the photon wave function using the data for the $e^+e^-$
annihilation, $e^+e^- \to\Upsilon(9460)$, $\Upsilon(10023)$, $\Upsilon(10036)$,
$\Upsilon(10580)$, $ \Upsilon(10865)$, $\Upsilon(11019)$, and predict partial
widths of the two-photon decays $\eta_{b0}\to\ggam$, $\chi_{b0}\to\ggam$,
$\chi_{b2}\to\ggam$ for the radial excitation states below $B\bar B$ threshold
($n\le 3$).
