Shankara's commentary on the Brahma Sutras (by Badarayana/Vyasa) represents his magnum opus—the text establishing Advaita Vedanta as a systematic philosophical school. The Brahma Sutras consist of 555 extremely terse aphorisms (sutras) requiring commentary to understand. Shankara's Bhashya (commentary) demonstrates extraordinary logical rigor, scriptural knowledge, and philosophical sophistication. The work has four chapters: Samanvaya (harmonization) establishes Brahman as taught by Upanishads; Avirodha (non-contradiction) refutes rival schools including Samkhya, Buddhism, Jainism, and Vaisheshika; Sadhana (practice) discusses meditation and spiritual discipline; Phala (result) describes liberation. Shankara's methodology combines shruti (scriptural authority) and yukti (logical reasoning). He employs adhyaropa-apavada (superimposition and subsequent denial)—provisionally accepting something for teaching purposes, then negating it at higher level. For instance, he first teaches Brahman as creator, sustainer, destroyer (useful for meditation), then reveals Brahman beyond all activity. The commentary resolves apparent contradictions between Upanishads: when one says "creation happened thus" and another says "there is no creation," Shankara explains different levels of teaching (vyavaharika vs paramarthika). It develops the doctrine that effect is non-different from cause (vivarta vada), explains Maya in sophisticated detail, and establishes that liberation comes through knowledge, not action. Historically, this work became THE definitive Advaitic interpretation. All subsequent Vedantic schools—Ramanuja, Madhva, Nimbarka, Vallabha—had to write their own Brahma Sutra commentaries specifically to counter Shankara's interpretation. The Bhashya spawned two major sub-schools within Advaita: Bhamati (Vachaspati Mishra) and Vivarana (Prakashatman), debating fine points of Shankara's teachings. Modern scholars consider it authentic Shankara and his most important philosophical work.