Acceptance of an offer is a manifestation of assent to the terms thereof made by the offeree in a manner invited or required by the offer. Acceptance by performance requires that at least part of what the offer requests be performed or tendered and includes acceptance by a performance which operates as a return promise.  (Restatement of Contracts 2^nd).

(1) An accord is a contract under which an obligee promises to accept a stated performance in satisfaction of the obligor's existing duty. Performance of the accord discharges the original duty.

(2) Until performance of the accord, the original duty is suspended unless there is such a breach of the accord by the obligor as discharges the new duty of the obligee to accept the performance in satisfaction. If there is such a breach, the obligee may enforce either the original duty or any duty under the accord.

(3) Breach of the accord by the obligee does not discharge the original duty, but the obligor may maintain a suit for specific performance of the accord, in addition to any claim for damages for partial breach.

Restatement of Contracts 2nd.

A contract is a legally binding agreement which recognises and governs the rights and duties of the parties to the agreement. (Wikipedia https://en.wikipedia.org/wiki/Contract)

Express Contract: an expressed contract is an actual agreement of the parties, the terms of which are openly uttered or declared at the time of making it, being stated distinct and explicit language, either orally or in writing.  Black's Law Dictionary.  

Implied Contract: an implied contract is one not created or evidenced by the explicit agreement of the parties, but inferred by the law, as a matter of reason and justice from their acts for conduct, the circumstances surrounding the transaction making it a reasonable, or even a necessary, assumption that a contract existed between them.  Black's Law Dictionary.

Executed and Executory Contracts: contracts are divided into executed and executory.  In an executed contract nothing remains to be done by either party, and the transaction is complete at the moment that the arrangement is made, and payment therefore is made on the spot.  In an executory contract, some future act is to be done, as where an agreement is made to build a house in six months, or to do an act on or before some future day, or to lend money upon a certain interest, payable at a future time.  Black's Law Dictionary.

Bilateral Contract: A term, used originally in the civil law, but now generally adopted, denoting a contract in which both the contracting parties are bound to fill fill obligations reciprocally towards each other; as a contract of sale, where one becomes bound to deliver the thing sold, and the other to pay the price of it.  Black's Online Law Dictionary. 

Unilateral Contract: A unilateral contract is one in which one party makes an express engagement or undertakes a performance, without receiving in return any express engagement or promise of performance from the other.  Black's Online Law Dictionary.

Note concerning standards of preference in interpretation: express terms are given greater weight than course of performance, course of dealing, and usage of trade, course of performance is given greater weight than course of dealing or usage of trade, and course of dealing is given greater weight than usage of trade.  Restatement of Contracts 2nd.

Expectation
Reliance
Restitution
Liquidated
Punitive
Specific Performance

(separate definitions for each of above)

Misunderstanding
Incapacity
Mistake
Fraud / Misrepresentation
Duress
Illegality
Unconscionability

(separate definitions for each of above)

Impossibility
Impracticability
Frustration of Purpose

(separate definitions for each of above)

An integrated agreement is a writing or writings constituting a final expression of one or more terms of an agreement.

(2) Whether there is an integrated agreement is to be determined by the court as a question preliminary to determination of a question of interpretation or to application of the parol evidence rule.

(3) Where the parties reduce an agreement to a writing which in view of its completeness and specificity reasonably appears to be a complete agreement, it is taken to be an integrated agreement unless it is established by other evidence that the writing did not constitute a final expression.

Restatement of Contracts, 2nd.

This is the common designation of Avery celebrated English statute, passed in 1677, adopted in modified form by all states in the US.  Its chief characteristic is the provision that no suit or action shall be maintain on certain classes of contracts or engagements unless there shall be a note or memorandum thereof in writing signed by the party to be charged or by his authorized agent.  Its object was to close the door to numerous frauds and perjuries.  (Black’s Law Dictionary).  Contracts that fall within the Statute of Frauds are unenforceable unless evidenced by a writing. The writing must: i) Be signed by the party against whom enforcement is sought; and ii) Contain the essential elements of the deal.  The writing need not be formal (i.e., receipts or correspondence can serve as memoranda). The essential elements may be in more than one writing only if one of the writings references the other(s). The writing need not be delivered to the party trying to enforce the contract. Even if it is lost or destroyed, it still operates to satisfy the Statute of Frauds, and its prior existence can be proved by oral evidence.

Most states require that the following five categories of contracts be evidenced by a writing:
Marriage - A contract made upon consideration of marriage;
Suretyship - A contract to answer for the debt or duty of another;
One year - A contract that cannot be performed within one year from its making;
UCC - Under the UCC, a contract for the sale of goods for a price of $500 or more; and
Real property contract - A contract for the sale of an interest in real property.