Contracts can be oral or written.

However, the “statute of frauds” requires that certain contracts be in writing in order to be enforceable.  For example, the sale of real estate and the sale of goods for a price more than $500 require a signed writing.  However, the contract itself does not have to be in writing.  A memorandum outlining the essential terms of the agreement might suffice.  Though this is very technical, it is good practice to memorialize all important agreements.