The paper introduces a new algorithm called Max-Min Hill-Climbing (MMHC) for learning the structure of Bayesian networks. MMHC combines ideas from local learning, constraint-based, and search-and-score techniques. It first reconstructs the skeleton of the Bayesian network using a local discovery algorithm called Max-Min Parents and Children (MMPC), and then performs a Bayesian-scoring greedy hill-climbing search to orient the edges. The algorithm is evaluated extensively against several prototypical and state-of-the-art algorithms, including PC, Sparse Candidate, Three Phase Dependency Analysis, Optimal Reinsertion, Greedy Equivalence Search, and Greedy Search. MMHC outperforms these algorithms in terms of both computational efficiency and reconstruction quality. The paper also discusses the theoretical advantages of MMHC over the Sparse Candidate algorithm and provides a detailed analysis of the algorithms' performance and complexity. The implementation of MMHC is available for public use.The paper introduces a new algorithm called Max-Min Hill-Climbing (MMHC) for learning the structure of Bayesian networks. MMHC combines ideas from local learning, constraint-based, and search-and-score techniques. It first reconstructs the skeleton of the Bayesian network using a local discovery algorithm called Max-Min Parents and Children (MMPC), and then performs a Bayesian-scoring greedy hill-climbing search to orient the edges. The algorithm is evaluated extensively against several prototypical and state-of-the-art algorithms, including PC, Sparse Candidate, Three Phase Dependency Analysis, Optimal Reinsertion, Greedy Equivalence Search, and Greedy Search. MMHC outperforms these algorithms in terms of both computational efficiency and reconstruction quality. The paper also discusses the theoretical advantages of MMHC over the Sparse Candidate algorithm and provides a detailed analysis of the algorithms' performance and complexity. The implementation of MMHC is available for public use.