This treatise investigates a number of problems related to treewidth and pathwidth of graphs. The main objective is to obtain good bounds on the complexity of determining the treewidth and pathwidth for various classes of graphs.Originating from the author's Ph.D. thesis, this monograph presents original own work. Nevertheless, many interesting perspectives beyond are presented. In total, the book is a smooth introduction to the topic of graphs of bounded treewidth. It will help to satisfy the strong interest among the algorithmic graph theory community in the theory pertaining to the topic. Particularly valuable is the thorough survey given of the relevant current literature.