Arminianism

Arminianism is a set of beliefs based on the theologian Jacobus Arminius. It is primarily known for its view on Soteriology. The doctrines held by Arminians were introduced in order to address several disagreements with Calvinism. The Five Articles of Remonstrance pointed out five main disagreements with Calvinist doctrines; Predestination, Total Depravity, God's Saving Grace, Atonement, and Perseverance of the Saints.

In additional to these five points, Arminian theology also heavily relies on another doctrine about Libertarian Free Will.

Conditional Election
Conditional Election is the Arminian view on Predestination. The doctrine states that man uses his free will to make the choice to follow God. God only foreknew that person's choice, and did not actually make the decision himself.

Prevenient Grace
Prevenient Grace, or more accurately called Universal Prevenient Grace, is the belief that God gives all people this specific grace, in order to restore their Free Will, so that they are able to choose God. Without this grace, most Arminians believe that man would be completely sinful, and unable to choose God. This doctrine is opposed to the Calvinism view of Total Depravity.

Resistible Grace
Resistible Grace is a doctrine stating that God's Saving Grace is resistible through man's free will. This is as opposed to the Calvinist view that God's saving grace is humanly irresistible. Both Calvinists and Arminians agree that people are capable of resisting God's Saving Grace, but Arminians believe that God cannot overcome that resistance, and it's only through people's free will that they are able to be saved.

Unlimited Atonement
Unlimited Atonement, of course referring to Jesus's Atonement for our sins, is the belief that Jesus's death covered all people. As opposed to the Calvinist view that Jesus's death only covered the sins of the elect, Arminians believe that His death covered all people's sins.

Uncertainty of Perseverance
Uncertainty of Perseverance is the most largely disputed point of Arminian doctrine. It is opposed to the Calvinist view of Perservance of the Saints, which states that God will never let someone lose their salvation. Uncertainty of Perservance, on the other hand, states that man's free will makes him capable of losing his salvation.

As mentioned above, this is the most disputed point of Arminianism. Many Arminians disagree with this doctrines, but are still considered Arminians nonetheless.

Libertarian Free Will
Libertarian Free Will is an essential part of Arminian theology. It states that all of man's choices are completely free from any constraint of human nature, and predetermination by God. Arminians believe that one of God's ultimate goals is to preserve man's free will.

History
Arminianism was started by Jacobus Arminius, and eventually named after him.