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Using a 73.6 pb-1 data sample of Υ(2S) events collected with the CLEO II detector at the Cornell Electron Storage Ring, we have investigated the hadronic transitions between the Υ(2S) and the Υ(1S). The dipion transition Υ(2S) → Υ(1S) π+π- was studied using two different analysis techniques. Selecting events in which Υ(1S) → e+e-, μ+μ- (‘‘exclusive’’ analysis), and using the Υ(1S) leptonic branching fractions world averages from the PDG review, we obtained Ɓ(Υ(2S) → Υ(1S) π+π-) =0.189±0.004±0.010, while using a method allowing Υ(1S) → anything (‘‘inclusive’’ analysis) we obtained Ɓ(Υ(2S) → Υ(1S) π+π-) = 0.196 ±0.002±0.010. The appropriate weighted average of the two measurements gives Ɓ(Υ(2S) → Υ(1S) π+π-) = 0.192±0.002±0.010. Combining the exclusive and inclusive results we derive the Υ(1S) leptonic branching fractions Bee = 0.0229±0.0008±0.0011 and Bμμ = 0.0249±0.0008±0.0013. We also studied Υ(2S) → Υ(1S) π0π0 and obtained Ɓ(Υ(2S) → Υ(1S) π0π0) = 0.092±0.006±0.008. Parameters of the π π system (dipion invariant mass spectra, angular distributions) were analyzed and found to be consistent with current theoretical models. Lastly, we searched for the η and single π0 transitions and obtained the 90% confidence level upper limits Ɓ(Υ(2S) → Υ(1S) η) < 0.0028 and Ɓ(Υ(2S) → Υ(1S) π0) < 0.0011.