1. An agreement between two or more parties creating obligations that are enforceable or otherwise recognizable at law <a binding contract>.
2. The writing that sets forth such an agreement <a contract is valid if valid under the law of the residence of the party wishing to enforce the contract>. 
Excerpt from William R. Anson’s Principles of the Law of Contract (Arthur L. Corbin ed., 3d Am. ed. 1919):
“The term contract has been used indifferently to refer to three different things:
(1) the series of operative acts by the parties resulting in new legal relations;
(2) the physical document executed by the parties as the lasting evidence of their having performed the necessary operative acts and also as an operative fact in itself;
(3) the legal relations resulting from the operative acts, consisting of a right or rights in personam and their corresponding duties, accompanied by certain powers, privileges, and immunities.
The sum of these legal relations is often called ‘obligation.’ The present editor prefers to define contract in sense (3) . . . .” 
Excerpt fromSamuel Williston’s A Treatise on the Law of Contracts (Walter H.E. Jaeger ed., 3d ed. 1957):
“A contract is a promise, or a set of promises, for breach of which the law gives a remedy, or the performance of which the law in some way recognizes as a duty. This definition may not be entirely satisfactory since it requires a subsequent definition of the circumstances under which the law does in fact attach legal obligation to promises. But if a definition were attempted which should cover these operative facts, it would require compressing the entire law relating to the formation of contracts into a single sentence.” 
Excerpt from John D. Calamari & Joseph M. Perillo’s The Law of Contracts (4th ed. 1998):
“The term ‘contract’ is also used by lay persons and lawyers alike to refer to a document in which the terms of a contract are written. Use of the word in this sense is by no means improper so long as it is clearly understood that rules of law utilizing the concept ‘contract’ rarely refer to the writing itself. Usually, the reference is to the agreement; the writing being merely a memorial of the agreement.” 
3. A promise or set of promises by a party to a transaction, enforceable or otherwise recognizable at law; the writing expressing that promise or set of promises <when the lessor learned that the rooms were to be used for the delivery of blasphemous lectures, he declined to perform his contract>. See Restatement (Second) of Contracts § 2 (1979).
Excerpt from John D. Calamari & Joseph M. Perillo’s The Law of Contracts 5 1.1, at 1-2 (4th ed. 1998):
“The promissory element present in every contract is stressed in a widely quoted definition: ‘A contract is a promise, or set of promises, for breach of which the law gives a remedy, or the performance of which the law in some way recognizes as a duty.’ [1 Samuel Williston, Contracts § 1.1 (4th ed. 1990).] This, like similar definitions, is somewhat misleading. While it is true that a promise, express or implied, is a necessary element in every contract, frequently the promise is coupled with other elements such as physical acts, recitals of fact, and the immediate transfer of property interests. In ordinary usage the contract is not the promise alone, but the entire complex of these elements.” 
4. Broadly, any legal duty or set of duties not imposed by the law of tort; especially, a duty created by a decree or declaration of a court <an obligation of record, as a judgment, recognizance, or the like, is included within the term “contract”>.
5. The body of law dealing with agreements and exchange <the general theory of contract>.
6. The terms of an agreement, or any particular term <there was no express contract about when the money was payable>.
7. Loosely, a sale or conveyance.
Excerpt from John Edward Murray Jr.’s Murray on Contracts (2d ed. 1974):
“Sometimes the word ‘contract’ is used to designate a transaction involving the exchange of goods or land for money. When money is exchanged for goods, this constitutes a sale. When money is exchanged for land, this constitutes a conveyance. Sales and conveyances may be the result of a previous contract but they are not the contracts themselves. There is no undertaking or commitment to do or refrain from doing anything in the future. This indispensable element of contract is missing.“ 
9. Loosely, an enforceable agreement between two or more parties to do or not to do a thing or set of things; a compact <when they finally agreed, they had a contract>. -contract, vb. – contractual, adj.
Excerpt from Sturges v. Crowninshield, 17 U.S. (4 Wheat) 122, 143 (1819):
“A contract is an agreement in which a party undertakes to do, or not to do, a particular thing.” 
“[Latin ‘from a contract] (17c.) Arising from a contract <action ex contractu>.” 
Equity Law is law which compels performance. It compels you to perform to the exact letter of any contract that you are under. So, if you have compelled performance, there must be a contract somewhere, & you are being compelled to perform under the obligation of the contract. Now this can only be a civil action – not criminal. In Equity Jurisdiction, you cannot be tried criminally, but you can be compelled to perform to the letter of a contract. If you then refuse to perform as directed by the court, you can be charged with contempt of court, which is a criminal action.
Contracts Must be Voluntary:
Under the Common Law, every contract must be entered into knowingly, voluntarily, & intentionally by both parties or it is void & unenforceable. These are characteristic- it must be based on substance. For example, contracts used to read, “For one dollar & other valuable considerations, I will paint your house, etc.” That was a valid contract. A contract must be based on substance. 
History Worth Remembering:
Arguably the most powerful passages on the purpose of the contract come from the works of John Locke, whose writings inspired the American, English, and French Revolutions. Locke was the most quoted authority on government in the 1760-1776 period prior to American independence. Thomas Jefferson was accused of plagiarizing Locke in certain sections of the Declaration of Independence by fellow Virginian delegate Richard Henry Lee.  Here are excerpts from Two Treatises of Civil Government:
On Civil Government – Ch. I:
Slavery is so vile & miserable an estate of man, & so directly opposite to the generous temper & courage of our nation, that it is hardly to be conceived, that an Englishman, much less a gentleman, should plead for it….
Second Treatise of Civil Government – Ch. IV “Of Slavery”:
THE natural liberty of man is to be free from any superior power on earth, & not to be under the will or legislative authority of man, but to have only the law of nature for his rule. The liberty of man, in society, is to be under no other legislative power, but that established, by consent, in the commonwealth; nor under the dominion of any will, or restraint of any law, but what that legislative shall enact, according to the trust put in it. Freedom then is not what Sir Robert Filmer tells us… ‘a liberty for every one to do what he lists, to live as he pleases, & not to be tied by any laws’: but freedom of men under government is, to have a standing rule to live by, common to every one of that society, & made by the legislative power erected in it; a liberty to follow my own will in all things… & not to be subject to the inconstant, uncertain, unknown, arbitrary will of another man…
This freedom from absolute, arbitrary power, is so necessary to, & closely joined with a man’s preservation, that he cannot part with it… for a man, not having the power of his own life, cannot, by compact (“compact” is an Old English term for “Contract” or “Agreement”), or his own consent, enslave himself to any one, nor put himself under the absolute, arbitrary power of another, to take away his life, when he pleases… for, whenever he finds the hardship of his slavery outweigh the value of his life, it is in his power, by resisting the will of his master, to draw on himself the death he desires.
… [T]he perfect condition of slavery, which is nothing else, but the state of war… between a lawful conqueror & a captive… Once compact (contract) enter between them, & make an agreement for a limited power on the one side, & obedience on the other, the state of war & slavery ceases, as long as the compact endures: for, as has been said, no man can, by agreement, pass over to another that which he hath not in himself, a power over his own life.
… we find among the Jews, as well as other nations, that men did sell themselves; but, it is plain, this was only to drudgery, not to slavery: for, it is evident, the person sold was not under an absolute, arbitrary, despotical power: for the master could not have power to kill him, at any time, whom, at a certain time, he was obliged to let go free out of his service; & the master of such a servant was so far from having an arbitrary power over his life, that he could not, at pleasure, so much as maim him, but the loss of an eye, or tooth, set him free, Exod. Xxi. 
Six Elements of a Legal Contract:
1. Offer – The offer is the very first part of creating a contract. It is the proposal a person or entity gives to another with the intention of entering into a valid contract. For example, Martha offers Karen fifty dollars a week in exchange for Karen to come in and clean her house.
2. Acceptance – A contract cannot legally exist without the offeree giving acceptance to the proposed offer. Without mutual consent from both parties however, there is no valid contract. Karen accepting Martha’s offer of fifty dollars for her services, & both Karen and Martha agreeing to go through with the exchange, is acceptance and mutual consent.
3. Consideration – The object, event, service, payment, etc. that the contract is created for is called the consideration of the contract, but both parties must give something of value. In this scenario, Karen will receive fifty dollars per week, and Martha’s house will be cleaned every week.
4. Legality of subject matter – Legality of subject matter refers to the fact that in order for a contract to be valid, it must be formed for a legal
purpose and has to follow any statutory regulations with respect to the contract created. It is legal for Martha to hire Karen to clean her house, but not to rob a bank.
5. Contractual capacity – A person has the contractual capacity to enter into a contract as long as they have the legal ability to. So if Karen
was a ten-year-old child, she would need her parent’s consent and signature in order to sign the contract, since Karen’s age & lack of experience overall makes her incapable contractually.
6. Contractual intent – Even with all of the above elements, a contract will not exist if the two parties did not subjectively want to enter
into a contract. On paper, Karen has signed the contract to clean Martha’s home weekly, and receives a weekly payment of fifty dollars. However, what if the only reason Karen signed the contract was because Martha threatened to show fabricated proof to Karen’s boss that she was stealing money from the company she works for?
Because of this situation, Karen did not demonstrate contractual intent to enter this relationship with Martha. Regardless of the type of contract created, all of these elements are crucial to a legally binding contract. Valid contracts are important to all businesses, & all facets of a business, whether the relationship is between the company & a customer, vendor, partner, etc. It is important to understand what a legal contract can adhere a person or business to, & understanding the basics can certainly clear up some of the confusion. 
Types of Contracts:
Absolute Simulated Contract – a simulated contract that the parties intend to be wholly ineffective.
Accessory Contract – entered into primarily for the purpose of carrying out a principal contract; especially for the purpose of obtaining by surety, mortgage, etc.
Adhesion Contract – a standard-form contract prepared by one party, to be signed by another party in a weaker position, usually a consumer, who adheres to the contract with little choice about the terms. — aka contract of adhesion; adhesive contract; adhesory contract; adhesionary contract; take-it-or-leave-it contract; leonine contract.
Aleatory Contract – where at least one party’s performance depends on some uncertain event that is beyond the control of the parties involved (i.e. insurance contracts and life annuities). — aka hazardous contract; wagering contract.
Alternative Contract – the performing party may elect to perform one of two or more specified acts to satisfy the obligation, usually permitting that party to choose the manner of performance. — aka alternative methods-of-performance contract.
Assessment Contract – wherein the payment of a benefit is dependent on the collection of an assessment levied on persons holding similar contracts.
Best Efforts Contract – wherein a party undertakes to use best efforts to fulfill the promises made rather than to achieve a specific result.
Bilateral Contract – wherein each party promises a performance, so that each party is an obligor on that party’s own promise. — aka mutual contract; reciprocal contract; (in civil law) synallagmatic contract.
Blanket Contract – covers a group of products, goods, or services for a fixed period.
Bona Fide Contract – wherein equity may intervene to correct inequalities and to adjust matters according to the parties’ intentions.
Build-to-Print Contract – requires the contractor to build a product according to exact technical specifications provided by the customer. — aka design specification contract.
Certain Contract – performed in a stipulated manner.
Collateral Contract – a side agreement made before or at the same time that relates to a contract that, if unintegrated, can be supplemented by evidence of the side agreement.
Commutative Contract – at the time it is formed, the parties’ obligations and advantages are certain and determinate so that nonperformance by either affords a defense to the other. — aka hypothetical contract.
Conditional Contract – enforceable only if another agreement is performed or if another particular prerequisite or condition is satisfied.
Consensual Contract – arising from the mere consensus of the parties, without any formal or symbolic acts performed to fix the obligation.
Construction Contract – sets forth the specifications for a building project’s construction, usually secured by performance and payment bonds to protect the owner and the subcontractors.
Consumer Contract – between a merchant seller and an individual who buys or contracts to buy goods to ensure the buyer intends to use them primarily for personal, family, or household purposes.
Continuing Contract – calls for periodic performances.
Contract for Sale – for the present transfer of property for a price (“contract of sale“), or to sell goods at a future time (“contract to sell“).
Contract for Services – for a job undertaken by an independent contractor, as opposed to an employee.
Contract in Restraint of Trade – limits the free exercise of business or trade (esp. stipulating that one who sells a business cannot open a similar business within a specified distance of the business being sold).
Contract of Insurance – See INSURANCE POLICY.
Contract of Pledge – wherein a debtor gives a creditor property to hold as security for a debt or the performance of a promise.
Contract of Record – declared by a court and entered into the court’s record (not a true contract).
5 Contract of service. 1. See CON’i n AC r on Si nvrw. 2. ice GMployment contract.
5 comract of subscription. See sunscnip’rion (3).
5$0ntract to pledge. (1866) 1. An agreement purport mg to create a present ledge without a bnilmcnt. 2. An agreement to make a uture bailment for the purpose or security. See PLEDGE (3).
5 centract to satisfaction. See satisfaction contract. 5 centract to sell. See contract for sale (2).
5 Contract uberrimaejidei ( oo-ber-a-mee fI-deed), (1916) A contract in which t e parties owe each other duties with the utmost good faith.
“in a certain restricted group of contracts good faith is peculiarly necessary owing to the relationship between the parties, and in these cases known as contracts uberrimae fidei -there is a full duty to disclose all material facts. The typical instance of such contracts is the contract of insurance. Here the duty to disclose all material facts to the insurer arises from the fact that many of the relevant circumstances are within the exclusive knowledge of one party, and it would be impossible for the insurer to obtain the facts necessary for him to make a proper calculation of the risk he is asked to assume without this knowledge.” P.S. Atiyah, An Introduction to the Law of Contract 221-22 (3d ed. 1981).
5 contract under hand. (18c) Archaic. A contract entered into by individual signature by a duly authorized person, as opposed to a contract executed under seal or by deed.
> contract under seal. (1827) A formal contract that requires no consideration and has the seal of the signer attached. 0 A contract under seal must be in writing or printed on paper or parchment and is conclusive between the parties when signed, sealed, and delivered. Delivery is made either by actually handing it to the other party (or party’s representative) or b stating an intention that the deed be operative even though it is retained in the possession of the party executing it. Modern statutes have mostly eliminated the special effects of a sealed contract. Also termed sealed contract; agreement under seal; special contract; deed; covenant; specialty; specialty contract; common-law spe~ cialty. See SEAL. Cf. sealed instrument under INSTRU
”The only formal contract of English law is the contract under seal, sometimes also called a deed and sometimes a specialty. it is the only formal contract, because it derives its validity neither from the fact of agreement, nor from the consideration which may exist for the promise of either party, but from the form in which it is expressed.” William R. Anson, Principles of the Law of Contract 82 (Arthur L. Corbin ed., 3d Am. ed. 1919).
“Contracts under seal also bear little resemblance to ordinary contracts, although here at least the liability is based on a promise. A contract under seal, that is to say a deed, . . . is a written promise or set of promises which derives its validity from the form, and the form alone, of the executing instrument. in point of fact the ‘form’ of the deed is nowadays surprisingly elastic. The only necessities are that the deed should be intended as such, and should be signed, sealed, and delivered. The seating, however, has now become largely a fiction, an adhesive water simplY being attached to the document in place at a genuine so» Similarly, ‘delivery’ is not literally necessary, provided th there is a clear intention that the deed should be op 18 rive.” P.S. Atiyah, An Introduction to the Law of Contra“ 31 (3d ed. 1981).