Action planning has always played a central role in Artificial Intelligence. Given a description of the current situation, a description of possible actions and a description of the goals to be achieved, the task is to identify a sequence of actions, i.e., a plan that transforms the current situation into one that satisfies the goal description. This monograph is a revised version of Malte Helmert's doctoral thesis, Solving Planning Tasks in Theory and Practice, written under the supervision of Professor Bernhard Nebel as thesis advisor at Albert-Ludwigs-UniversitAt Freiburg, Germany, in 2006. The book contains an exhaustive analysis of the computational complexity of the benchmark problems that have been used in the past decade, namely the standard benchmark domains of the International Planning Competitions (IPC). At the same time, it contributes to the practice of solving planning tasks by presenting a powerful new approach to heuristic planning. The author also provides an in-depth analysis of so-called routing and transportation problems. All in all, this book will contribute significantly to advancing the state of the art in automatic planning.