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 $\Upsilon(3S)\rightarrow \pi^+\pi^- h_b$. Show Partial Abstract