Extractive summarization, a pivotal task in natural language processing, aims to distill essential content from lengthy documents efficiently. Traditional methods often struggle with capturing the nuanced interdependencies between different document elements, which is crucial to producing coherent and contextually rich summaries. This paper introduces Multi-Element Contextual Hypergraph Extractive Summarizer (MCHES), a novel framework designed to address these challenges through an advanced hypergraph-based approach. MCHES constructs a contextual hypergraph where sentences form nodes interconnected by multiple types of hyperedges, including semantic, narrative, and discourse hyperedges. This structure captures complex relationships and maintains narrative flow, enhancing semantic coherence across the summary. The framework incorporates a Contextual Homogenization Module (CHM), which harmonizes features from diverse hyperedges, and a Hypergraph Contextual Attention Module (HCA), which employs a dual-level attention mechanism to focus on the most salient information. The innovative Extractive Read-out Strategy selects the optimal set of sentences to compose the final summary, ensuring that the latter reflects the core themes and logical structure of the original text. Our extensive evaluations demonstrate significant improvements over existing methods. Specifically, MCHES achieves an average ROUGE-1 score of 44.756, a ROUGE-2 score of 24.963, and a ROUGE-L score of 42.477 on the CNN/DailyMail dataset, surpassing the best-performing baseline by 3.662%, 3.395%, and 2.166% respectively. Furthermore, MCHES achieves BERTScore values of 59.995 on CNN/DailyMail, 88.424 on XSum, and 89.285 on PubMed, indicating superior semantic alignment with human-generated summaries. Additionally, MCHES achieves MoverScore values of 87.432 on CNN/DailyMail, 60.549 on XSum, and 59.739 on PubMed, highlighting its effectiveness in maintaining content movement and ordering. These results confirm that the MCHES framework sets a new standard for extractive summarization by leveraging contextual hypergraphs for better narrative and thematic fidelity.