Graphs are known structures with many applications in various fields including computer science and information visualization. Drawing graphs makes understanding the meaning of graphs easy by geometrically representation of them. Many graph drawing algorithms have been presented in the literature. Most of them draw graphs on an unbounded surface. However, there are applications in which it is required to draw graphs on a prescribed size area. For example, consider a VLSI circuit which should be designed on a U-shaped PCB with prescribed size, or consider a software in which one would like to show a graph on a prescribed size area. In this book, we examine the complexity of this problem, and introduce new algorithms for drawing planar graphs on 2D surfaces which are bounded by simple polygons. The content of this book is suitable for use in advanced undergraduate and graduate level courses on algorithms, graph drawing, information visualization and computational geometry. The book will also serve as a useful reference for researchers and software developers in the field of graph drawing, information visualization, VLSI design and CAD.