A complete picture of hadron spectroscopy is important for the understanding of the degrees of freedom inside the hadron in the medium energy region. This study will bridge the gap between the hadron/pion picture in the low-energy region and the quark/gluon picture in the high-energy region. However, while only the low-energy resonances have been well identified, the high-energy excited states are broad and overlapping, so can only be disentangled with Partial Wave Analysis (PWA). The present PWA still has ambiguities due to the lack of experimental data, especially data using a polarized neutron target.The G14 experiment in Hall B of Jefferson Lab was designed and conducted to measure polarization observables from both polarized proton and neutron targets. The reaction channels studied in this dissertation are the single pion (γn → pπ − ) and double pion (γp → pπ + π − , and γn → nπ + π − ) photo-production. The E asymmetry in the single pion channel shows good agreement at lower energy with the prediction from two PWA groups: SAID from George Washington University and Bonn-Gatchina from University of Bonn. At higher energy, there is a big discrepancy between the experimental result and PWA prediction. This result is significant since the "missing resonances" are in this higher energy region. The polarization observables(I , P z , P z ) in the two-pion channel with polarized neutron target are the first results that have been measured, and these three observables(I , P z , P z ) in the two-pion channel with polarized proton target are compared with a previous CLAS experiment (G9a). The results are essential for the study of high-energy excited states since this channel has a bigger cross section than the single pion channel in the high-energy region.i