  Using a data sample of $\Upsilon(2S)$ events collected with the CLEO II
detector at the Cornell Electron Storage Ring, we have investigated the
hadronic transitions between the $\Upsilon(2S)$ and the $\Upsilon(1S)$. The
charged dipion transition $\Upsilon(2S)\to \Upsilon(1S)\pi^+\pi^-$ was studied
using two different analysis techniques. Selecting events in which
$\Upsilon(1S)$ decays into a $\mu\mu$ or $ee$ lepton pair(``exclusive''
analysis), we measured the branching fraction of B=0.189+-0.004+-0.009, while
using a method allowing $\Upsilon(1S)$ to decay into anything (``inclusive''
analysis) we found B=0.0196+-0.002+-0.010. The appropriate average of the two
measurements gives B=0.0192+-0.002+-0.010. Combining the exclusive and
inclusive results we derive the $\Upsilon(1S)$ leptonic branching ratios
B_{ee}=0.0229+-0.0008+-0.0011 and B_{\mu\mu}=0.0249+-0.0008+-0.0013 We also
studied $\Upsilon(2S)\to \Upsilon(1S)\pi^0\pi^0$ and obtained the branching
fraction of B=0.092+-0.006+-0.007. Parameters of the $\pi\pi$ system (dipion
invariant mass spectra, angular distributions) were analyzed and found to be
consistent with current theoretical models. Lastly, we searched for the $\eta$
and single $\pi^0$ transitions and obtained the upper limits of 0.0028 and
0.0011 respectively.
