Exact solutions to nonlinear evolution equations (NEEs) play an important role in nonlinear physical science, since the characteristics of these solutions may well simulate real-life physical phenomena. One of the benefits of finding new exact solutions to such nonlinear partial differential equations (PDEs) is to give a better understanding on the various characteristics of the solutions. The main task of this work is to show that our proposed methods, improved tanh and sech methods, are very efficient in solving various types of NEEs and PDEs including special equations than using classical tanh and sech methods. This efficiency is because of their rich with the multiple traveling wave solutions than classical tanh and sech methods. From the obtained results, we can not only recover the previous solutions obtained by some authors but also obtain some new and more general solitary wave, singular solitary wave and periodic solutions. Illustrating the theory of nonlinear transmission lines (NLTLs), showing the ability of NLTL to generate solitons and solving the model equation of NLTL in presence of loss are other tasks of this book.