Vanguard is a supplement for Magic: The Gathering that debuted in Arena's Summer Season of 1997.
Vanguard is also a format, and the card type associated with it.
The Vanguard format allows players to play with a special extra "card" that modifies the rules of the game just for them. You enter a Vanguard game with a normal constructed deck in the format of your choice, plus a preselected Vanguard card. Players must agree on which format (Standard, Modern, Legacy or Vintage) they will use to build their decks.
The oversized (3" x 5") Vanguard cards aren't played like regular cards. Instead, each player chooses one of the character cards before the match begins and plays under the conditions set by that card.  
A Vanguard card modifies your starting (and maximum) hand size, as well as your starting life total. It also contains one or more abilities. Sometimes they're abilities that you can play; sometimes they're abilities that just change aspects of the game. Any abilities printed on a Vanguard card work exactly like those of an in-play Magic card. Note, however, that Vanguard cards are colorless, aren't permanents, aren't in play, and aren't even really cards — so they can't be affected by spells or abilities.
The result of a cooperative effort between Wizards of the Coast's R&D and Events departments, Vanguard was designed specifically for casual play. The cards were released in four 8-card sets, the first two were designed together. Series 1 could also be obtained in the Vanguard Gift Box. The intent was to use the Arena League as a test market for the concept of supplemental products.  As it turned out, Vanguard was a huge success. Nearly 5,000 joined Arena during the first season, the biggest increase in league history, yet. From there, the decision to release the second group of eight cards in early 1998 (Winter Season) was simple. The third set appeared in late 1998 (Autumn Season), and the fourth in the Spring Season of 1999.   
Vanguard cards Ertai and Gerrard from Series 1
The oversized Vanguard cards all had the same layout: adjustments to the starting and maximum hand size in the lower left, adjustments to the starting life total in the lower right, and any other effects of having the card in play described in the text box. Cards from the first three sets picture a character from the Weatherlight Saga. While the two first sets featured the central characters, the latter set depicted charachters from the periphery of the tale. The fourth set depicted characters from Urza's Saga. 
Four cards were bagged together with The Duelist magazine:
- Duelist #19 - Series 1 Gerrard
- Duelist #33 - Series 3 Multani
- Duelist #37 - Series 4 Urza
- Duelist #47 - Series 4 Mishra
From the Comprehensive Rules
(Shadows over Innistrad
(April 8, 2016))
- 311.1. Vanguard is a card type seen only on nontraditional Magic cards. Only the Vanguard casual variant uses vanguard cards. See rule 902, “Vanguard.”
- 311.2. Vanguard cards remain in the command zone throughout the game. They’re not permanents. They can’t be cast. If a vanguard card would leave the command zone, it remains in the command zone.
- 311.3. Vanguard cards have no subtypes.
- 311.4. A vanguard card may have any number of static, triggered, and/or activated abilities. As long as a vanguard card is in the command zone, its static abilities affect the game, its triggered abilities may trigger, and its activated abilities may be activated.
- 311.5. The owner of a vanguard card is the player who started the game with it in the command zone. The controller of a face-up vanguard card is its owner.
- 311.6. Each vanguard card has a hand modifier printed in its lower left corner. This is a number preceded by a plus sign, a number preceded by a minus sign, or a zero. This modifier is applied to the starting hand size and maximum hand size of the vanguard card’s owner (normally seven). The resulting number is both how many cards that player draws at the beginning of the game and his or her maximum hand size.
- 311.7. Each vanguard card has a life modifier printed in its lower right corner. This is a number preceded by a plus sign, a number preceded by a minus sign, or a zero. This modifier is applied as the starting life total of the vanguard card’s owner (normally 20) to is determined. See rule 103.3.
From the Comprehensive Rules
(Shadows over Innistrad
(April 8, 2016))
- 902.1. In the Vanguard variant, a vanguard card allows each player to play the role of a famous character. Each player will have one face-up vanguard card whose abilities and other characteristics affect the game. The Vanguard variant uses all the normal rules for a Magic game, with the following additions.
- 902.2. A Vanguard game may be a two-player game or a multiplayer game.
- 902.3. In addition to the normal game materials, each player needs a vanguard card. Each vanguard card is placed face up next to its owner’s library before the game begins. All vanguard cards remain in the command zone throughout the game.
- 902.4. Each player’s starting life total is 20 plus or minus the life modifier of his or her vanguard card.
- Example: The life modifier of a player’s vanguard card is -3. That player’s starting life total is 17.
- 902.5. Each player’s starting hand size is seven cards, as modified by the hand modifier of his or her vanguard card.
- 902.5a If a player takes a mulligan in a Vanguard game, just like in a normal game, that player shuffles his or her hand back into his or her library, then draws a new hand of one fewer cards than he or she had before. (In a multiplayer game, a player’s first mulligan is for the same number of cards as he or she had before.) See rule 103.4.
- Example: The hand modifier of a player’s vanguard card is +2. That player starts the game with a hand of 9 cards. If the player takes a mulligan, he or she draws a new hand of 8 cards. The next mulligan is for 7 cards, and so on.
- 902.5b A player’s maximum hand size is seven, as modified by the hand modifier of his or her vanguard card.
- Example: The hand modifier of a player’s vanguard card is -1. That player’s maximum hand size is six. If that player has more than six cards in his or her hand as the cleanup step begins, he or she will discard all but six of them.
- 902.6. The owner of a vanguard card is the player who started the game with it in the command zone. The controller of a face-up vanguard card is its owner.
- 902.7. Any abilities of a face-up vanguard card in the command zone function from that zone. The card’s static abilities affect the game, its triggered abilities may trigger, and its activated abilities may be activated.
- Each player has one Vanguard card in effect for the duration of each duel.
- Each event will have its own specific rules for the method and frequency of selecting the card(s) to be used.
- Each player's Vanguard card is in effect throughout the duel; Vanguard cards may not be targeted, removed from play, or otherwise affected during play.
- Unless specifically stated otherwise, the Vanguard card's effect extend only to the controller of the card (and his or her permanents, if applicable).
- The Vanguard card being used by each player must be visible at all times to all players.
Since May 2005, Vanguard Avatars were also used as in casual games for Magic Online. You added one of them to your deck before play, and at the start of the game, the avatar card from your deck started in play for you and applies the modifications listed on it. Starting with Zendikar, rules text and hand size/life total modifications for vanguard avatars was discontinued. Nowadays, you may continue to play the vanguard format with previously avatars. Both old and new avatars can still be used to represent you in-game. 
- ↑ Magic Arcana. (September 23, 2002.) "Vanguard Series 1", Daily MTG, magicthegathering.com, Wizards of the Coast. [dead link]
- ↑ Magic Arcana. (October 09, 2002.) "Vanguard Series 2", Daily MTG, magicthegathering.com, Wizards of the Coast. [dead link]
- ↑ Andy Collens, 1998. New Year, New Vanguard, the Duelist # 22, 1998
- ↑ Mark Rosewater. (August 30, 2010.) "Thank You Sir, May I Have Another", Daily MTG, magicthegathering.com, Wizards of the Coast. [dead link]
- ↑ Jesse Decker, 1999. Third Vanguard Set Charges into Arena's Autum Season, the Duelist # 33
- ↑ Editorial Staff, 1999. Get ready for Vanguard, the Duelist # 37
- ↑ Magic Arcana. (October 14, 2008.) "Vanguard Portraits", Daily MTG, magicthegathering.com, Wizards of the Coast. [dead link]
- ↑ Magic Online Vanguard