Magic: The Gathering Commander
Commander is a series of supplemental Magic: the Gathering card game products. Its mechanics are derived from a fan-created format known as "Elder Dragon Highlander (EDH)".

Gameplay
Commander is a format where players construct 100-card decks, with each card except basic lands appearing no more than once. The format is primarily played with four players, each with their own deck. Players also choose a legendary creature or Planeswalker to be their "Commander" or "General" (a Planeswalker must be designated as allowed to be used as a Commander), which begins the game in the "Command Zone". Each player's deck is based and built around their Commander's colors. In addition to the same losing conditions that exist in a normal game of Magic, each player starts the game with 40 life points instead of 20, and a player may lose if he or she is dealt 21 or more total points of combat damage from a single Commander throughout the game. Commander is most commonly played in groups of four, but larger groups do happen. A one-on-one variant on the Commander rule set has been rising in popularity.

Commander also has its own "banned list" of cards, separate from any other format. A list of the recommended banned cards in the format can be found on Wizard's official page here

Variants 

 Commander is often played in conjunction with existing gamemodes like Two-Headed Giant, Planechase, and Archenemy. 
 Duel Commander got its origins from Level 5 judge Kevin Desprez, who brought the initial idea of Elder Dragon Highlander to France from the USA, before it spread across Europe and now over the rest of world. The game is played by two opponents only, starts with 20 health points, and obeys the same rules as a regular Magic The Gathering game, one commander (or commanders with Partner ability) plus 99 (or 98 with Partners) cards in the starting library. The mulligan system is the same as for sanctioned formats, and the construction rules follow the same color identity rule as the multiplayer version does. The rules and updates are currently published on a Facebook page using notes.
 Magic Online 1v1 Commander is Wizards of the Coast's attempt at creating a variant of Commander. The format utilizes a banlist created by Wizards that differs from that of the Rules Committee and is played almost exclusively on Magic: The Gathering Online. 
 Brawl is Wizards of the Coast's second attempt to create a Commander variant. Brawl utilizes all cards that are currently legal in Standard and has a rotation schedule similar to Standard's. The format is commonly played as a sanctioned event on Magic: The Gathering Online, but also has a following that plays the format physically. The format was not received by the players due to the rotation of older cards in standard.

Commander sets

Commander 2011
Magic: The Gathering Commander was released on June 17, 2011. It consisted of five preconstructed decks, each containing three foil oversized legendary creature cards. This set is notable in that it was the first set printed outside of the normal booster pack expansions to have functionally new cards. The set introduced 51 new cards, made specifically for multi-player games.

Each deck is built around a new legendary creature and a distinct mechanical theme. In addition to the intended Commander, they include two other new legendary creatures.
 Heavenly Inferno (white/black/red, commanded by ) features a variety of Angels, Demons, and Dragons that Kaalia can put directly into play, and numerous creature destruction effects. Its other new Legendary creatures are  and .
 Mirror Mastery (blue/red/green, commanded by ) uses large amounts of mana acceleration to cast powerful spells and creatures for Riku to copy. Its other new Legendary creatures are  and .
 Counterpunch (black/green/white, commanded by ) is constructed around the dual themes of creature tokens and +1/+1 counters. Its other new Legendary creatures are  and .
 Political Puppets (red/white/blue, commanded by ) uses Zedruu to gain cards and life while earning good will and turning opponents against each other. Its other new Legendary creatures are  and .
 Devour for Power (green/blue/black, commanded by ) fills graveyards with creatures in order to power up The Mimeoplasm and other synergistic cards. Its other new Legendary creatures are  and .

Commander's Arsenal
Commander's Arsenal is a set with 18 premium foil cards, 10 oversized premium foil cards, card sleeves, a life counter, and tokens for keeping track of in-game effects. The set was released on November 2, 2012. Each card in the set was the first edition of that card to receive premium foil treatment, the first to be printed in the modern frame, and/or received special art.

Commander 2013
Commander 2013 was released on November 1, 2013. It introduced five new pre-constructed decks, each built around one of the three-colored "shards".  51 new cards were printed for Commander 2013, including five that introduced the mechanic Tempting offer, which allows opponents to duplicate the card's effect but at the cost of granting its controller a larger effect. Each of the Commanders interacts with the Command Zone, either offering a benefit for playing the commander repeatedly or giving the player a benefit while still remaining in the Command Zone.

Evasive Maneuvers (green/white/blue, commanded by ) has a tap/untap and exile-and-return theme.
Eternal Bargain (white/blue/black, commanded by ) features the two themes of life gain and artifacts.
Mind Seize (blue/black/red, commanded by ) features an instant and sorcery theme alongside cards that punish opponents for drawing. 
Power Hungry (black/red/green, commanded by ) features a creature token theme, sacrificing them for a benefit.
Nature of the Beast (red/green/white, commanded by ) features a creature token theme.

Commander 2014
Commander 2014 was released on November 7, 2014. It introduced five new pre-constructed decks, each built around one of the five colors.  61 new cards were printed for Commander 2014, including five that introduced the Lieutenant mechanic, which gives a bonus for the creature if you also control your Commander, and the first ever Planeswalkers that can be your Commander.

Forged In Stone (white, commanded by ) with an equipment theme.
Peer Through Time (blue, commanded by )
Sworn To Darkness (black, commanded by 
Built From Scratch (red, commanded by ) themed around artifacts.
Guided By Nature (green, commanded by ) themed around elves.

Commander 2015
Commander 2015 was released on November 10, 2015. It introduced five new pre-constructed decks, built around "enemy" two-color combinations. 55 new cards were printed, including new commanders that utilized "experience counters" to grow more powerful as the game progressed. Other new cards introduced the Myriad mechanic, which allowed a single creature to attack every opponent simultaneously.
Call the Spirits (white/black, commanded by ) themed around enchantments.
Seize Control (blue/red, commanded by ) themed around instants and sorceries.
Plunder the Graves (black/green, commanded by ) themed around sacrificing creatures and returning creatures from the graveyard.
Wade into Battle (red/white, commanded by ) themed around giants.
Swell the Host (green/blue, commanded by ) themed around creating multiple smaller creatures and increasing their power.

Commander 2016
Commander 2016 was released on November 11, 2016. It introduced five new pre-constructed decks, built around four-color combinations. The new "Partner" mechanic allows two legendary creatures, both with Partner, to serve as your commander. 56 new cards were printed, including the first 4-color legendary creatures.
Entropic Uprising (blue/black/red/green, commanded by ) with a "windmill" theme that gains benefits from opponents drawing or discarding cards.
Open Hostility (black/red/green/white, commanded by ) with a focus on combat damage.
Stalwart Unity (red/green/white/blue, commanded by ) with a focus on "Group Hug" effects that benefit all players and encourage playing politics with the other players.
Breed Lethality (green/white/blue/black, commanded by ) with a focus on +1/+1 counters and multiplying those counters.
Invent Superiority (white/blue/black/red, commanded by ) with a focus on artifacts.

Commander Anthology
Commander Anthology was released on June 9, 2017. It is a boxed re-release of four pre-constructed decks, one from each of the first four years of Commander sets.
 Heavenly Inferno (2011) (white/black/red, commanded by )
Evasive Maneuvers (2013) (green/white/blue, commanded by )
Guided By Nature (2014) (green, commanded by )
Plunder the Graves (2015) (black/green, commanded by )

Commander 2017
Commander 2017 was released on August 25, 2017. Starting with Commander 2017, Commander sets are reduced from five to four preconstructed theme decks (without reducing the number of new cards) and will be built around themes instead of focusing on color combinations. Commander 17 is a tribal set, with each deck focussing on one creature type. The new "Eminence" mechanic grants a benefit while a Commander is in play or in the command zone, with each commander having an additional effect while they are on the battlefield.
 Draconic Domination  (all five colors, commanded by ) a dragon deck. 
 Feline Ferocity  (green/white, commanded by ) a Cat deck, with an equipment theme that encourages improving a single creature at a time.
 Vampiric Bloodlust  (red/white/black, commanded by ) a vampire deck.
 Arcane Wizardry (blue/black/red, commanded by ) a wizard deck.

Commander Anthology Volume 2 
Commander Anthology Volume 2 was announced on February 14, 2018 for release on June 8, 2018.  Like the previous year's Commander Anthology, Volume 2 will be a boxed re-release of four pre-constructed decks. It contains the following decks:
Devour for Power (2011) (green/blue/black, commanded by )
Built from Scratch (2014) (red, commanded by )
Wade into Battle (2015) (red/white, commanded by )
Breed Lethality (2016) (green/white/blue/black, commanded by )

Commander 2018 
Commander 2018 was announced on February 14, 2018 for release on August 10, 2018. It sees the return of Planeswalkers as Commanders. It contains the following decks: 

 Exquisite Invention (blue/red, commanded by Saheeli, the Gifted) an artifact deck that produces artifact tokens.
 Subjective Reality (white/blue/black, commanded by Aminatou, the Fateshifter) with a theme of controlling the top card of the deck.
 Nature's Vengeance (black/red/green, commanded by Lord Windgrace) a land themed deck.
 Adaptive Enchantment (white/blue/green, commanded by Estrid, the Masked) an enchantment themed deck.

Commander 2019 
Commander 2019 was announced on February 21, 2019 for a scheduled release on August 23, 2019 
. The following decks were previewed:
 Faceless Menace (blue/green/black, commanded by Kadena, Slinking Sorcerer) with the overarching theme of playing face-down 'Morph' creatures and benefiting of playing creatures.
 Mystic Intellect (red/blue/white, commanded by Sevinne, the Chronoclasm) a spell-heavy deck focused on casting spells multiple times, using 'Flashback' to cast spells again from the graveyard.
 Primal Genesis (red/green/white, commanded by Ghired, Conclave Exile) a token deck aiming to create a bunch of token creatures and 'Populate' them.
 Merciless Rage (red/black, commanded by Anje Falkenrath) Designed around discarding cards and benefiting of this by employing the 'Madness' keyword for value.