*352 LIPEZ, Judge:

This appeal involves a petition to compel arbitration of claims for alleged breaches of express and implied warranties and for negligence in connection with the construction of a school building. The school authority, as owner of the building, had filed suit against the architect, the general contractor, a subcontractor and a materialman. The defendant architect then brought this petition. The court below ordered arbitration as to all of the parties except the materialman and the defendant subcontractor appealed. We reverse as to the appellant.

On June 20, 1967, the Cumberland-Perry Area Vocational-Technical School Authority (Authority) contracted with Bogar & Bink (Architect) for the design of the Authority’s school buildings in Mechanicsburg, Pennsylvania. The general construction contract was awarded to H. B. Alexander & Son, Inc., (Alexander). On June 10, 1969, Alexander contracted with Suburban Roofing Co., Inc., (Suburban) for construction and installation of the roof of the school building. In performing the work, Suburban purchased materials from the predecessor in interest to the Celotex Corporation. Construction was completed in 1970, and the final payment was made on October 20 of that year.

On February 20, 1976, after certain alleged defects in construction of the roof had become evident, the Authority filed a writ of summons against the Architect, Alexander, Suburban and Celotex, seeking damages for the defects. On April 22, 1977, the Authority filed a complaint against the above defendants alleging breach of express and implied warranties and negligence by each of them. On May 31, 1977, the Architect petitioned the Court of Common Pleas of Cumberland County to stay the proceedings and order arbitration between the Authority on one hand, and the Architect, Alexander, Suburban and Celotex on the other, pursuant to the contracts between the Authority and the Architect, the Authority and Alexander, and Alexander and Suburban.

*353 The trial court ordered a consolidated arbitration among all parties except Celotex, and Suburban appealed. We conclude that the court below, by requiring arbitration with parties not in contractual privity with Suburban in effect remade the contract. For the reasons which follow, we vacate the order as to Suburban.

Arbitration is a matter of contract, and parties to a contract cannot be compelled to arbitrate a given issue absent an agreement between them to arbitrate that issue. Lincoln University v. Lincoln University Chapter of AAUP, 467 Pa. 112, 119, 354 A.2d 576, 580 (1976); Schoellhammer’s Hatboro Manor, Inc., v. Local Joint Executive Board, 426 Pa. 53, 58, 231 A.2d 160, 162 (1967). Even though it is now the policy of the law to favor settlement of disputes by arbitration and to promote the swift and orderly disposition of claims, Children’s Hospital v. Am. Arb. Ass’n, 231 Pa.Super. 230, 234, 331 A.2d 848, 850 (1974), arbitration agreements are to be strictly construed and such agreements should not be extended by implication. Emmaus Municipal Auth. v. Eltz, 416 Pa. 123, 125, 204 A.2d 926, 927 (1964).

Three contracts are involved in the case before us: (1) The contract between the Authority and the Architect (hereinafter referred to as the “Architect’s Contract”); (2) the contract between the Authority and Alexander (the “General Contract”); and (3) the contract between Alexander and Suburban (the “Subcontract”).

The Architect’s Contract contains the following provision: 11.1 All claims, disputes and other matters in question arising out of or relating to this agreement or the breach thereof shall be decided by arbitration in accordance with the Construction Industry Arbitration Rules of the American Arbitration Association then obtaining (Emphasis added.)

Substantially the same provision is contained in the General Contract. The Subcontract incorporates all of the terms of the General Contract and contains a provision which, in effect, requires the settlement of disputes by *354 arbitration. 1 The lower court erred in holding Suburban bound by an arbitration provision of a contract (viz., the Architect’s Contract) to which it was not party, and which contract was not incorporated into any contract to which it was party (the Subcontract). The arbitration provision contained in the Subcontract is enforceable only against the parties thereto.

The court below found, in contradiction of Suburban’s position, that Suburban was bound, under the Subcontract and the General Contract as incorporated therein, to arbitrate with the Authority the dispute over the roof defects. We need not reach a determination of that issue on this appeal, since it is not the Authority which has petitioned for arbitration, but rather the Architect. The Architect’s petition for a stay and referral to arbitration must be based upon the arbitration clause in the Architect’s Contract, because that is the only one of the three contracts relevant to this matter to which the Architect is party. Suburban is not party to the Architect’s Contract; the arbitration clause contained therein is not enforceable against Suburban. The Architect attempts to stand in the shoes of the Authority by contending that, since all parties to the original action (except Celotex) have allegedly agreed to arbitration with the Authority, any party may enforce the arbitration clause in its own contract against all such other parties. We do not agree. It is a basic principle that a contract cannot legally bind persons not party thereto. See generally 1 S. Williston, Contracts § 1 (3d ed. 1957 and Supp.1978).

Persons cannot compel arbitration of a disagreement between or among parties who have not contracted to arbitrate that disagreement between or among themselves. Lincoln University v. Lincoln University Chapter of AAUP, *355 supra ; Schoellhammer’s Hatboro Manor, Inc. v. Local Joint Executive Board, supra. In this case, the only contract to which Suburban is party is the Subcontract between Suburban and Alexander. Since the Architect is not party to the Subcontract, the Architect may not avail itself of the arbitration clause contained therein. Even if we assume arguendo that Suburban is bound to arbitrate the roofing dispute with the Authority, the Architect’s position vis-a-vis Suburban is not strengthened. Just as the Architect is not party to the Subcontract so is it not party to the General Contract, and the arbitration provision contained therein is not enforceable by the Architect against anyone. For the lower court to order Suburban into arbitration on the petition of the Architect is to remake the Subcontract and the Architect’s Contract with reference to other litigants in this action who were not parties thereto; this a court may not do. That portion of the order of the court below requiring Suburban to join in arbitration is therefore vacated. 2

. Children’s Hospital of Phila. v. American Arb. Ass’n, 231 Pa.Super. 230, 331 A.2d 848 (1974), cited by the court below, is readily distinguishable. In that case, identical clauses in separate contracts between the Hospital and four prime contractors provided for arbitration of certain disputes. The Hospital’s motion for arbitration of a dispute between it and each of the contractors was granted, because each contractor was party to a contract with the movant Hospital requiring arbitration.

. The Subcontract actually provides that any method of dispute settlement provided for by the Contract shall control and that if none be so provided, Suburban will be bound to procedural rules of the National Joint Board for the Settlement of Jurisdictional Dispute in the Construction Industry. Suburban was thereby bound to proceed under the arbitration provision of the General Contract as incorporated into the Subcontract.