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 First of all, I would like to thank my adviser, Blaine Norum, for his guidance in my PhD study, and for providing me with great freedom to pursue my ideas. I really appreciate his help to get me in his group in my fourth year, and to introduce me to the G14 experiment and the HDice group at Jefferson Lab. During the time I was doing the experiment and the data analysis at Jefferson Lab, he drove to the Lab almost every week to have a meeting with me, this helped me to keep a good pace with my project. During the last year, when I moved back to UVa, Blaine and I were working together on the explanation of an unexpected peak in the missing momentum plot. Even though the peak turned out to be caused by the gaps of the CLAS detectors, his way to pursue an explanation for the peak and his attitude to be careful for a new discovery have taught me a very good lesson of how to do research. I would like to thank Donal Day and Kent Paschke for serving on my thesis committee, and for their precious comments on my thesis. I also would like to thank Nilanga Liyanage and Krishni Wijesooriya for giving me a chance to work with them on nuclear physics and medical physics. None of this work would have been possible without the help from the people in G14 collaboration and the HDice g...