Mathematical Study of Multi-Fields Inflation and Perturbation Theory

I would like to thank Almighty Allah, the most beneficent and merciful, to give me the opportunity to complete my this work successfully. I wish to express my heartiest gratitude to my supervisor Dr. Cong-Feng Qiao, Professor of the College of Physical Sciences, (GUCAS), for his invaluable advice and encouraging support. I wish to thank my Co-Supervisor and advisor Dr. Yun-Song Piao for the inspiration, support and guidance, for the infinite degrees of freedom, and for proving that success in science is not irreconcilable with having a life. He not only supervised me to materialize the work but also showed me the way to think in different dimensions and work steadily from the very beginning of a research. Special thanks to my friends and colleagues for their interest and support of my research work. Many thanks go to so many others for helping me get through the difficult times, and for all the emotional support they provided. Finally, the greatest thanks to my Parents, and my wife for her love and my both sons.