In Why I am Not an Arminian, Robert Peterson and Michael Williams present a tough critique of Arminian doctrine and a solid defense of Calvinist theology. Unlike so many other writings on this divisive topic, this work is irenic and good-natured. They make clear near the outset that Arminians are brothers and sisters in Christ. While clearly stating their view that Arminian theology makes serious doctrinal errors on important theological points, they wisely refrain from making the overblown charge of heresy. In the introduction, they write,
“You see, calling someone a heretic is serious business. Heresy is not merely doctrinal error; it is damnable error. The heretic so mangles the gospel of Jesus Christ that it no longer communicates the grace of God in Jesus Christ. Heresy is such a corruption of the grace of God in Christ that it invalidates either Jesus as he Savior or grace as the way of salvation. The Arminian tradition does neither. The Arminian Christian believes that Jesus Christ is God come in the flesh to save sinners and that the saving work of Christ comes to the sinner by way of the grace of God received through faith. Whatever issues relevant to salvation we disagree upon, let us agree on this: the Calvinist and the Arminian are brothers in Christ.” 
The authors are wise to understand the distinction between heresy and incorrect doctrine, and they should be commended for recognizing, in no uncertain terms, that Arminian theology is within orthodoxy.
Despite their charitable attitude towards their ideological counterparts, Peterson and Williams pull no punches in their critique of the Arminian tradition. They begin their work with a brief history of the debate between Augustine and Pelagius. Both of these thinkers endorsed monergism- which is the view that only one agent acts authoritatively in salvation. While Augustine defended divine monergism, with God being the sole actor in salvation, Pelagius defended human monergism (note: there is some debate about this point. Pelagius’s works are only available in bits via critiques from other writers like Augustine, who is not known for being charitable when quoting opponents. Nevertheless, Pelagius certainly focused much more attention on human effort in salvation than did Augustine). Pelagius was condemned in 417. Soon after, the so-called Semi-Pelagians John Cassian and Vicent of Lerins defended the view that human nature is weakened but not disabled by sin. However, the first step towards God is taken by man, though grace is still needed if salvation is to be attained. This view defends synergism, the view that there are two actors in salvation- both God and man- working together.
This discussion is important not only because it sets up the historical context of this debate, but also because it reveals a fundamentally unfair charge made by many anti-Arminians that Arminian theology is Pelagian or Semi-Pelagian. As a matter of fact, Arminian theology affirms that sin has so corrupted the human nature that God must make the first move to make individuals receptive to the Gospel. This view is actually a modification of Augustine and so is called Semi-Augustinianism by Peterson and Williams. This is the view that was affirmed in the Synod of Orange in 529.
In addition to the historical overview, however, Peterson and Williams focus a great deal of attention on important Biblical passages that touch on the core differences between Arminians and Calvinists. They have good discussions on predestination, perseverance, and irresistible grace. Unfortunately, however, I think that they seriously botch the issue of free will.
To begin, they assume that free will is the foundation of Arminian theology. “…for Arminius and the Arminian tradition, human freedom is axiomatic. Because of this the freedom of the human will serves as a kind of grid through which all other notions and doctrines must pass in order to be accepted. That which might qualify or question human free will must be rejected. The assumption of the unblemished integrity of human free will leads Arminian theology toward indeterminist incompatibilism: divine sovereignty and true human freedom are incompatible, and human beings are free; therefore, God cannot sovereignly govern human history, events or personal destinies.” [137-8]
First of all, I think this is a caricature of the Arminian position. As Roger Olson points out, God’s goodness and justice are actually axiomatic for the Arminian position. Arminian theology protects God’s character by denying that He has anything to do with evil, instead attributing this evil to the sinful choices of free creatures. Moreover, Arminian theology takes seriously the Biblical affirmation that God desires the salvation of all men. While it may be true that some Arminians advocate the view because they want to salvage indeterministic free will, it is unfair to label this issue as the ‘axiomatic, non-negotiable’ factor in Arminian theology.
Secondly, Peterson and Williams make the classic false dichotomy between libertarian human freedom and divine sovereignty. It is simply silly to say that Arminian theology entails that God is not sovereign, since He sovereignly decided to create free human agents. If God freely decides to create agents who can freely decide what they will do, His sovereignty is not limited but rather enhanced. Indeed, Calvinism often seems to deny the very possibility that God could decide to create agents with libertarian free will, which seems to be a limitation on God’s freedom itself. In any case, the Molinist account of divine foreknowledge and providence adequately demonstrates that God can sovereignly order the world through free creatures.
Thirdly, the authors seem to imply that libertarians believe that we can literally always choose otherwise. But this is a crass oversimplification of the view. Few libertarians contend that every choice we make is completely free.
Finally, the authors contend that the Bible supports a compatibilist understanding of freedom, but they never defend this view philosophically. While I respect the author’s focus on Scripture, I doubt that Peterson and Williams can allay the suspicions of libertarians like myself who believe that so-called compatibilist freedom is a vacuous concept. Moreover, all of the scriptural passages cited by the authors to demonstrate how God molds history and works all things towards His ends through human free choices simply supports the Molinist view that is often advanced by Arminians.
Nevertheless, other than a weak discussion on the nature of freedom, Peterson and Williams do a marvelous job explaining their disagreements with Arminianism and offering the Calvinist alternative. Their book should be praised for its irenic spirit and civil tone, as well as for its formidable scholarship. I recommend that you read this book along with the companion volume- Why I am Not a Calvinist by Jerry Walls and Joseph Dongell- for a good overview of this important debate.