Fast Downward is a classical planning system based on heuristic search, capable of handling general deterministic planning problems encoded in the propositional fragment of PDDL2.2. Unlike other planners like HSP and FF, Fast Downward does not directly use the propositional PDDL representation but translates the input into a multi-valued planning task, making implicit constraints explicit. This translation allows Fast Downward to exploit hierarchical decompositions of planning tasks for computing its causal graph heuristic, which is different from traditional heuristics based on ignoring negative interactions of operators. The article provides a comprehensive overview of Fast Downward's approach to solving multi-valued planning tasks, extending the discussion of the causal graph heuristic to tasks involving axioms and conditional effects. It introduces novel techniques for search control, including preferred operators, deferred evaluation of heuristic functions, and multi-heuristic best-first search. Efficient data structures for fast state expansion and a new non-heuristic search algorithm called focused iterative-broadening search are also described. Fast Downward has been successful, winning the "classical" track of the 4th International Planning Competition at ICAPS 2004, following in the footsteps of planners like FF and LPG. Experiments show that it performs well on benchmarks from earlier planning competitions, providing insights into the usefulness of new search enhancements. The article begins with an introduction to the problem of transportation planning, using a simple example to illustrate the hierarchical approach humans often use to solve such tasks. It then discusses the concept of causal graphs and their role in hierarchical planning, highlighting the importance of acyclicity in causal graphs for hierarchical decomposition. The article also reviews related work, including the use of causal graphs and domain transition graphs in previous research. The Fast Downward planning system is described in detail, including its three main components: translation, knowledge compilation, and search. The translation component converts PDDL2.2 tasks into multi-valued planning tasks, the knowledge compilation component generates data structures for efficient search, and the search component implements three different search algorithms: greedy best-first search, multi-heuristic best-first search, and focused iterative-broadening search. The article concludes with a formal introduction to multi-valued planning tasks, defining the problem and its state space, and discussing the knowledge compilation process, which includes computing domain transition graphs, causal graphs, successor generators, and axiom evaluators.Fast Downward is a classical planning system based on heuristic search, capable of handling general deterministic planning problems encoded in the propositional fragment of PDDL2.2. Unlike other planners like HSP and FF, Fast Downward does not directly use the propositional PDDL representation but translates the input into a multi-valued planning task, making implicit constraints explicit. This translation allows Fast Downward to exploit hierarchical decompositions of planning tasks for computing its causal graph heuristic, which is different from traditional heuristics based on ignoring negative interactions of operators. The article provides a comprehensive overview of Fast Downward's approach to solving multi-valued planning tasks, extending the discussion of the causal graph heuristic to tasks involving axioms and conditional effects. It introduces novel techniques for search control, including preferred operators, deferred evaluation of heuristic functions, and multi-heuristic best-first search. Efficient data structures for fast state expansion and a new non-heuristic search algorithm called focused iterative-broadening search are also described. Fast Downward has been successful, winning the "classical" track of the 4th International Planning Competition at ICAPS 2004, following in the footsteps of planners like FF and LPG. Experiments show that it performs well on benchmarks from earlier planning competitions, providing insights into the usefulness of new search enhancements. The article begins with an introduction to the problem of transportation planning, using a simple example to illustrate the hierarchical approach humans often use to solve such tasks. It then discusses the concept of causal graphs and their role in hierarchical planning, highlighting the importance of acyclicity in causal graphs for hierarchical decomposition. The article also reviews related work, including the use of causal graphs and domain transition graphs in previous research. The Fast Downward planning system is described in detail, including its three main components: translation, knowledge compilation, and search. The translation component converts PDDL2.2 tasks into multi-valued planning tasks, the knowledge compilation component generates data structures for efficient search, and the search component implements three different search algorithms: greedy best-first search, multi-heuristic best-first search, and focused iterative-broadening search. The article concludes with a formal introduction to multi-valued planning tasks, defining the problem and its state space, and discussing the knowledge compilation process, which includes computing domain transition graphs, causal graphs, successor generators, and axiom evaluators.