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Search is a keyword action. It was introduced on Demonic Tutor in Alpha. 
From the Comprehensive Rules (Ravnica Allegiance (January 25, 2019))
- 701.18. Search
- 701.18a To search for a card in a zone, look at all cards in that zone (even if it's a hidden zone) and find a card that matches the given description.
- 701.18b If a player is searching a hidden zone for cards with a stated quality, such as a card with a certain card type or color, that player isn't required to find some or all of those cards even if they're present in that zone.
Example: Splinter says "Exile target artifact. Search its controller's graveyard, hand, and library for all cards with the same name as that artifact and exile them. Then that player shuffles their library." A player casts Splinter targeting Howling Mine (an artifact). Howling Mine's controller has another Howling Mine in her graveyard and two more in her library. Splinter's controller must find the Howling Mine in the graveyard, but may choose to find zero, one, or two of the Howling Mines in the library.
- 701.18c If a player is instructed to search a hidden zone for cards that match an undefined quality, that player may still search that zone but can't find any cards.
Example: Lobotomy says "Target player reveals their hand, then you choose a card other than a basic land card from it. Search that player's graveyard, hand, and library for all cards with the same name as the chosen card and exile them. Then that player shuffles their library." If the target player has no cards in their hand when Lobotomy resolves, the player who cast Lobotomy searches the specified zones but doesn't exile any cards.
- 701.18d If a player is searching a hidden zone simply for a quantity of cards, such as "a card" or "three cards," that player must find that many cards (or as many as possible, if the zone doesn't contain enough cards).
- 701.18e If the effect that contains the search instruction doesn't also contain instructions to reveal the found card(s), then they're not revealed.
- 701.18f If searching a zone is replaced with searching a portion of that zone, any other instructions that refer to searching the zone still apply. Any abilities that trigger on a library being searched will trigger.
Example: Aven Mindcensor says, in part, "If an opponent would search a library, that player searches the top four cards of that library instead." Veteran Explorer says "When Veteran Explorer dies, each player may search their library for up to two basic land cards and put them onto the battlefield. Then each player who searched their library this way shuffles it." An opponent who searched the top four cards of their library because of Veteran Explorer's ability would shuffle the entire library.
- 701.18g If an effect offers a player a choice to search a zone and take additional actions with the cards found, that player may choose to search even if the additional actions are illegal or impossible.
- 701.18h If multiple players search at once, each of those players looks at the appropriate cards at the same time, then those players decide in APNAP order (see rule 101.4) which card to find.
From the glossary of the Comprehensive Rules (Ravnica Allegiance (January 25, 2019))
- To look at all cards in a stated zone and possibly find a card that matches a given description. See rule 701.18, "Search."