Many problems encountered in applied mathematics or mathematical physics can be modeled by using differential equations under different boundary conditions. In this regard, linear and nonlinear partial differential equations are often used because of their strong capacity to describe and formulate many real-world problems governed by dynamical phenomena. There are many different methods to solve linear and nonlinear problems arising from different studies in various disciplines. However, due to lack of general existence theorems for establishing solutions, scientists have to seek alternative approaches and methods. In this context, the present work demonstrates different methods and approaches to obtain solutions to some class of differential equations given under different boundary conditions. The present book, where contemporary developments in the area of boundary value problems is shared, can be beneficial to advanced undergraduates, graduate students and researchers who are interested in the area of differential equations.