Free offer of the gospel
The free offer of the Gospel, sometimes called the well-meant offer of the gospel, in Christian theology, is the offer of salvation in Jesus Christ to all people. It is generally accepted by Calvinists, but rejected by a few small Reformed denominations, such as the Evangelical Presbyterian Church in Australia and the Protestant Reformed Churches in America, and also by some English Strict Baptists of longer standing, such as John Gill and, later, the Gospel Standard Strict Baptists.
The phrase "the free offer" has not always been used in the same way throughout history. One historical usage is found in the Westminster Shorter Catechism, Question 31, "What is Effectual Calling" which ends "he doth persuade and enable us to embrace Jesus Christ, freely offered to us in the gospel." Due to its presence in the commonly used catechism, this phrase would for centuries have been familiar to most Scottish Christians and to some in other countries as well. In this context, the phrase is used in connection with God's elect, whom he effectually calls.
Modern day usage of the phrase "the free offer" is used synonymously with the phrase "the well-meant offer." Modern debates over the topic generally deal with the phrase as defined by John Murray in his OPC statement "The Free Offer of the Gospel." 
General Call vs. Free Offer
The free offer of the gospel builds on, but is not the same as, the general call, which can be found in the Canons of Dort. This states: "Moreover, it is the promise of the gospel that whoever believes in Christ crucified shall not perish but have eternal life. This promise, together with the command to repent and believe, ought to be announced and declared without differentiation or discrimination to all nations and people, to whom God in his good pleasure sends the gospel" (II.5).
This distinction is important as it distinguishes those who deny the free offer from those who might deny the general call.
The free offer is related to the belief that "God not only delights in the penitent but is also moved by the riches of his goodness and mercy to desire the repentance and salvation of the impenitent and reprobate." 
Based upon this belief, John Murray concludes that: "The full and free offer of the gospel is a grace bestowed upon all... The grace offered is nothing less than salvation in its richness and fullness. The love or lovingkindness that lies back of that offer is not anything less; it is the will to that salvation." 
This idea has caused dispute in Calvinist circles concerning whether or not an evangelist can sincerely say that God desires the salvation of everyone in attendance and is waiting and hoping for them to "repent and believe." The concern is that this message is no different than the Arminian delivery. The heart of the matter, according to the majority report submitted to the General Assembly of the Orthodox Presbyterian Church in 1948, is "whether it can properly be said that God desires the salvation of all men." Those taking the negative position are sometimes labeled Hyper-Calvinists.
This label is disputed, however, in that some who deny the free offer accept the idea of a "general call". David J. Engelsma states: "Ours is a denial that arises out of the Reformed faith itself, that is in perfect harmony with all aspects of the Reformed faith (including the serious, external call to all who come under the preaching!), and that is made for the sake of the maintenance of the Reformed faith. It is not a rejection of the church's duty to preach the gospel to all men indiscriminately. We believe that the many must be called."
John Gerstner, a former student of Murray, states: "With tears in my heart, I nevertheless confidently assert that they erred profoundly in The Free Offer of the Gospel and died before they seem to have realized their error which . . . still does incalculable damage to the cause of Jesus Christ and the proclamation of His Gospel." 
- Modern Moderate Calvinism
- Westminster Shorter Catechism
- Orthodox Presbyterian Church statement
- "The Free Offer of the Gospel" (the majority report submitted to the General Assembly of the Orthodox Presbyterian Church in 1948) by John Murray with a foreword by R. Scott Clark.
- "All house and no doors: A Critique of Hyper-Calvinism" by C. Matthew McMahon
- "Is Denial of the Well-Meant Offer Hyper Calvinism?" by David J. Engelsma
- "A History of Hypo-Calvinism" by Marc Carpenter
- "The Free Offer of the Gospel: Is It Biblical and Reformed?" from Free Church Witness
- "Calvinists and the Free Offer of the Gospel" - primary source quotations compiled by Colin Maxwell
- "Murray on the Free Offer: A Review by Matthew Winzer"
- "History of the Free Offer"
- "Is Denial of the 'Well-Meant Offer' Hyper-Calvinism?"
- "A History of Hypo-Calvinism"
- "The Banner of Truth vs. Calvinism"
- "God Makes a Wish: That Each and Every Sinner Might Be Saved" - A Brief Essay by Robert Gonzales Jr.