Commander is an official Magic: The Gathering™ Format, that emphasises group dynamics, high variance and self-expression.
Typically played in groups of 4, players battle in a free-for-all game, starting at 40 life and piloting singleton 100-card decks led by a Commander.
A commander is typically a single Legendary Creature that leads your deck. It begins the game outside of your 99-card deck in the Command Zone and completes your 100-card deck. It is therefore available for you to play every game. This leads to interesting deck-building decisions and additionally your commander determines what cards may be used in constructing your deck by Color Identity. Sometimes your commander can be a Planeswalker if it says so, or you can have 2 If they have Partner with, Partner, Doctors Companion or Friends Forever in which case both count towards colour identity. Here are some examples:
Atla Palani, Nest Tender could be a commander since she is a Legendary Creature.
Saheeli the Gifted is a planeswalker but can be a Commander since it's written on the card, similar to Shorikai, Genesis Engine.
Vial Smasher the Fierce & Akiri, Line Slinger could both be the commander of a single deck since they have "Partner."
Ukkima, Stalking Shadow and Cazur, Ruthless Stalker can both be the commander of a single deck, but only with each other since they have "Partner with".
The Fugitive Doctor and Sarah Jane Smith can both be the commander of a single deck since one is a "Time Lord Doctor" and the other has "Doctor's Companion"
Cecily, Haunted Mage and Elmar, Ulvenwald Informant can both be the commander of a single deck since they both have "Friends Forever"
This is the special zone the Commander of a deck begins the game in. The Commander is available from the beginning of the game and it can be cast just like any other card in your hand from this zone, as long as you pay an extra 2 generic mana for each time you've cast it from the command zone this game.
What happens if my commander dies? - This is a more complicated rule, so here's an extract from the Official Commander Website.
"If a commander would ever be in the graveyard or in exile, and it was put there since the last time state-based actions were checked, its owner may put it back in the command zone."
This is a fancy way of saying if your commander dies or is exiled, after the effect that put it there has been resolved, you can put it back in the command zone.
As an example: If Elenda, the Dusk Rose is your commander, you will normally cast her for 2WB the first time. If she dies, you will trigger her ability, put her back in the Command Zone from the Graveyard and then resolve her trigger for the Vampire Tokens. The next time you would cast her from the Command Zone, she will cost 4WB.
There's also a separate rule for if your commander goes to the Library or Hand:
"If a commander would be put into its owner’s hand or library from anywhere, its owner may put it into the command zone instead."
This is a similar rule except that the commander is put into the command zone instead of the hand or library, and not after the ability or spell has been resolved. This is an important rule, and one to remember. If you would put your commander from your hand into your deck, you can apply this rule and put it into the Command Zone instead.
Colour Identity is a unique feature of Commander that further distinguishes this format from others. For a card to be legal for your commander deck its colour identity must fall within your Commander's Colour Identity. Colour identity comes from any mana symbols in any part of the card, including its mana cost, rules text and any colour identifiers. This includes the backside of any double-faced cards. Do note that colour identity only has effects on deck construction and not in-game.
A simple rule of thumb would be if you see a coloured mana symbol on the card, add that colour to its colour identity. Unfortunately, there are exceptions, that everyone has to remember. Below are some examples if you want to try but its not essential to get this right immediately and it will become easier with time.
Goliath Sphinx has blue mana symbols in its casting costs and no other coloured mana symbols, so it has a Blue colour identity. Nice and Simple!
Izzet Charm has Blue and Red mana symbols in its casting cost, so it has a Blue-Red colour identity. Still easy!
Jodah, Archmage Eternal has Blue, Red and White in his casting cost, but it has all 5 coloured mana symbols in its rules text, so it has a 5-Colour identity, often called WUBRG (White, Blue, Black, Red, Green). So a deck with Jodah as the Commander could play any card! Neat!
Daemogoth Titan has hybrid Black/Green mana symbols in its casting cost. Since hybrid counts as both colours in Commander, Daemogoth Titan has a Black-Green colour identity. This is a tough one since you have to know how the Commander format treats hybrid mana, and this is still considered a contentious issue among some players.
Spellskite at first glance may appear as a colourless card, but it has a Blue Phyrexian mana symbol in its textbook, so it has a Blue colour identity.
Lands aren't treated as having any colour in Magic, but the basic land types on them are used to determine their colour identity.
Temple Garden has a White-Green Colour Identity since it is both a Plains and a Forest.
Mana Confluence can make all 5 colours of mana, but with no basic land types and no mana symbols present, it has a Colourless Colour Identity.
Reminder Text is not used to determine colour identity, so Crypt Ghast has only Black Colour Identity, not Black-White.
Cards that mention other colours by name will not have their colour identity changed, so Red Elemental Blast has a Red colour identity, even if it mentions "blue" in its text.
Double-faced cards are simple, with a little exception:
Throne of the Grim Captain is colourless on its front side but has a black colour indicator symbol just before the word "legendary" on its type line on the backside. Both sides of a card are used to determine the colour identity and colour indicators are considered as well, so it has a Black Colour identity.
This double-faced rule doesn't apply to Meld cards (since they're not a full card on the back), so The Mightstone and Weakstone has a Colourless colour identity even if it is half of Urza, Planeswalker
This is a simple but important rule for gameplay.: If any player would take 21 or more points of combat damage from a single commander card, throughout the game, that player immediately dies. Because of this commander damage is usually tracked
Commander damage DOES include:
21 or more combat damage at one time.
Multiple instances of combat damage over the entire game adding to 21 or more combat damage.
Combat damage from a commander while somebody besides the owner of that commander controls it.
21 combat damage from your OWN COMMANDER.
It does NOT include:
Non-combat damage.
Damaged caused by copies/clones of a commander.
Combat damaged of a Partner/Doctor-Companion/Friends Forever pair combined.