702.85. Rebound

• 702.85a Rebound appears on some instants and sorceries. It represents a static ability that functions while the spell is on the stack and may create a delayed triggered ability. "Rebound" means "If this spell was cast from your hand, instead of putting it into your graveyard as it resolves, exile it and, at the beginning of your next upkeep, you may cast this card from exile without paying its mana cost."
• 702.85b Casting a card without paying its mana cost as the result of a rebound ability follows the rules for paying alternative costs in rules 601.2b and 601.2e-g.
• 702.85c Multiple instances of rebound on the same spell are redundant.

Rules Translation

• 702.85a You'll only find Rebound on instants or sorceries, it is a static always-on ability so long as the spell is in the process of being cast. What it means is, if you play it from your hand, rather than sending it to the graveyard, it resolves, is exiled and at the beginning of your next upkeep, you may cast it again without paying its mana cost.
• 702.85b Casting the spell for free can still be modified such that it isn't free such as by cards that make spells cost more.
• 702.85c If a spell somehow gets a second instance of Rebound, it still is only able to be cast during the next upkeep just once.

Notes from the Rise of the Eldrazi FAQ

• If a spell with rebound that you cast from your hand is countered for any reason (due to a spell like Cancel, or because all of its targets are illegal), the spell doesn't resolve and rebound has no effect. The spell is simply put into your graveyard. You won't get to cast it again next turn.
• If you cast a spell with rebound from anywhere other than your hand (such as from your graveyard due to Sins of the Past, from your library due to cascade, or from your opponent's hand due to Sen Triplets), rebound won't have any effect. If you do cast it from your hand, rebound will work regardless of whether you paid its mana cost (for example, if you cast it from your hand due to Maelstrom Archangel).
• If a replacement effect would cause a spell with rebound that you cast from your hand to be put somewhere else instead of your graveyard (such as Leyline of the Void might), you choose whether to apply the rebound effect or the other effect as the spell resolves.
• Rebound will have no effect on copies of spells because you don't cast them from your hand.
• If you cast a spell with rebound from your hand and it resolves, it isn't put into your graveyard. Rather, it's exiled directly from the stack. Effects that care about cards being put into your graveyard won't do anything.
• At the beginning of your upkeep, all delayed triggered abilities created by rebound effects trigger. You may handle them in any order. If you want to cast a card this way, you do so as part of the resolution of its delayed triggered ability. Timing restrictions based on the card's type (if it's a sorcery) are ignored. Other restrictions are not (such as the one from Rule of Law).
• If you are unable to cast a card from exile this way (because there are no legal targets for it, for example), or you choose not to, nothing happens when the delayed triggered ability resolves. The card remains exiled for the rest of the game, and you won't get another chance to cast the card. The same is true if the ability is countered (due to Stifle, perhaps).
• If you cast a card from exile this way, it will go to your graveyard when it resolves or is countered. It won't go back to exile.