This book is the doctoral thesis of the author submitted to University of Hyderabad in 2008. In this he has proved an extension of Tunnell's theorem which was done partially by Prof. Dipendra Prasad, Tata Institute of Fundamental Research, Mumbai in 1994. Prasad himself gave a complete proof of the theorem in 2007, but using completely different techniques used in the proof appearing in this dissertation. Later in the book, the author uses this theorem to do some interesting "counting of characters". Even though the calculations appearing in this book are long, they are not so complicated and showcase some interesting methods for solving epsilon factor related calculations. This thesis has already appeared in publication as two articles, the first one in Journal of Number theory in 2008 and the second one in the Proceedings of Indian Academy of Sciences (Mathematical Sciences) in 2011. But as usual, since the journal articles are short and compact missing several interesting in between arguments, this book is hopefully more useful to the beginners in representation theory involving computations in epsilon factors.