In this book the author presents some techniques for exploring trees and graphs. He illustrates the linear search technique and the backtracking technique, and as instances of tree exploration methods he presents various algorithms for parsing subclasses of context-free languages. He also illustrates some tree and graph exploration and manipulation methods by presenting, among others, algorithms for visiting trees, evaluating Boolean expressions, proving propositional formulas, computing paths in graphs, and performing string matching. This book has been used for advanced undergraduate and graduate courses on automata and formal languages, and assumes some prior exposure to the basic notions in that area. Sample programs are presented in Java and Prolog.