Which contractual element involves mutual agreement between parties?

The element that involves mutual agreement between parties is the offer and acceptance. This is foundational to contract law, as it establishes that one party makes a proposal (the offer) and the other party agrees to it (the acceptance). This mutual agreement signifies the willingness of both parties to enter into a binding contract. Without this agreement, there can be no contract, as there is no indication that both parties have reached a consensus on the terms of their arrangement.

Consideration, while integral to a contract, refers to what each party stands to gain or lose and does not directly speak to the mutual agreement aspect. Intention to create legal relations pertains to the intention of both parties to have their agreement enforceable by law, which is a separate consideration. Legality of purpose ensures that the contract is for a lawful purpose, but again, this is distinct from establishing mutual agreement. Thus, the option that most precisely addresses the concept of mutual agreement is indeed offer and acceptance.