Classical Arminianism (sometimes titled Reformed Arminianism or Reformation Arminianism) is the theological system that was presented by Jacobus Arminius and maintained by some of the Remonstrants; its influence serves as the foundation for all Arminian systems. A list of beliefs is given below:
Depravity is total: Arminius states "In this [fallen] state, the free will of man towards the true good is not only wounded, infirm, bent, and weakened; but it is also imprisoned, destroyed, and lost. And its powers are not only debilitated and useless unless they be assisted by grace, but it has no powers whatever except such as are excited by Divine grace."
Atonement is intended for all: Jesus's death was for all people, Jesus draws all people to himself, and all people have opportunity for salvation through faith.
Jesus's death satisfies God's justice: The penalty for the sins of the elect is paid in full through Jesus's work on the cross. Thus Christ's atonement is intended for all, but requires faith to be effected. Arminius states that "Justification, when used for the act of a Judge, is either purely the imputation of righteousness through mercy… or that man is justified before God… according to the rigor of justice without any forgiveness." Stephen Ashby clarifies: "Arminius allowed for only two possible ways in which the sinner might be justified: (1) by our absolute and perfect adherence to the law, or (2) purely by God's imputation of Christ's righteousness."
Grace is resistible: God takes initiative in the salvation process and His grace comes to all people. This grace (often called prevenient or pre-regenerating grace) acts on all people to convince them of the Gospel, draw them strongly towards salvation, and enable the possibility of sincere faith. Picirilli states that "indeed this grace is so close to regeneration that it inevitably leads to regeneration unless finally resisted."  The offer of salvation through grace does not act irresistibly in a purely cause-effect, deterministic method but rather in an influence-and-response fashion that can be both freely accepted and freely denied.
Man has free will to respond or resist: Free will is limited by God's sovereignty, but God's sovereignty allows all men the choice to accept the Gospel of Jesus through faith, simultaneously allowing all men to resist.
Election is conditional: Arminius defined election as "the decree of God by which, of Himself, from eternity, He decreed to justify in Christ, believers, and to accept them unto eternal life."God alone determines who will be saved and his determination is that all who believe Jesus through faith will be justified. According to Arminius, "God regards no one in Christ unless they are engrafted in him by faith."
God predestines the elect to a glorious future: Predestination is not the predetermination of who will believe, but rather the predetermination of the believer's future inheritance. The elect are therefore predestined to sonship through adoption, glorification, and eternal life.
Christ's righteousness is imputed to the believer: Justification is sola fide. When individuals repent and believe in Christ (saving faith), they are regenerated and brought into union with Christ, whereby the death and righteousness of Christ are imputed to them for their justification before God.
Eternal security is also conditional: All believers have full assurance of salvation with the condition that they remain in Christ. Salvation is conditioned on faith, therefore perseverance is also conditioned. Apostasy (turning from Christ) is only committed through a deliberate, willful rejection of Jesus and renunciation of saving faith. Such apostasy is irremediable.
The Five articles of Remonstrance that Arminius's followers formulated in 1610 state the above beliefs regarding (I) conditional election, (II) unlimited atonement, (III) total depravity, (IV) total depravity and resistible grace, and (V) possibility of apostasy. Note, however, that the fifth article did not completely deny perseverance of the saints; Arminius, himself, said that "I never taught that a true believer can… fall away from the faith… yet I will not conceal, that there are passages of Scripture which seem to me to wear this aspect; and those answers to them which I have been permitted to see, are not of such as kind as to approve themselves on all points to my understanding."Further, the text of the Articles of Remonstrance says that no believer can be plucked from Christ's hand, and the matter of falling away, "loss of salvation" required further study before it could be taught with any certainty.
The core beliefs of Jacobus Arminius and the Remonstrants are summarized as such by theologian Stephen Ashby:
1) Prior to being drawn and enabled, one is unable to believe… able only to resist.
2) Having been drawn and enabled, but prior to regeneration, one is able to believe… able also to resist.
3) After one believes, God then regenerates; one is able to continue believing… able also to resist.
4) Upon resisting to the point of unbelief, one is unable again to believe… able only to resist