  We present studies in bottomonium spectroscopy carried out with samples of
$(98\pm1)$ million $\Upsilon(2S)$ and $(121\pm1)$ million $\Upsilon(3S)$ events
recorded with the BaBar detector at the PEP-II asymmetric-energy $e^+ e^-$
collider at SLAC. Precise measurements of the branching fractions for
$\chi_{b1,2}(1P, 2P)\rightarrow \gamma \Upsilon(1S)$ and
$\chi_{b1,2}(2P)\rightarrow \gamma \Upsilon(2S)$ transitions, and searches for
radiative decay to the $\eta_b(1S)$ and $\eta_b(2S)$ states are performed using
photons that have converted into an $e^+ e^-$ pair. In addition, we summarize
the results of a search for the spin-singlet partner of the $\chi_{bJ}(1P)$
triplet, the $h_b(1P)$ state of bottomonium, in the transitions
$\Upsilon(3S)\rightarrow \pi^0 h_b$ and $\Upsilon(3S)\rightarrow \pi^+\pi^-
h_b$.
