Question: I know the basic difference between Arminianism and Calvinism in the soteriology subject, but when Molinism comes I can't grasp the core doctrines that it teaches. I'm not asking for which is better, just a concise, easy, and helpful definition of each one without too much philosophical blather.

Answer: 
Extract from [William Lane Craig](https://www.reasonablefaith.org/writings/question-answer/molinism-vs.-calvinism/) answering a question on the complexity of Molinism :

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> Actually, I have no problem with certain classic statements of the Reformed view. For example, the Westminster Confession (Sect. III) declares that
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> *God from all eternity did by the most wise and holy counsel of his own will, freely and unchangeably ordain whatsoever comes to pass; yet so as thereby neither is God the author of sin; nor is violence offered to the will of creatures, nor is the liberty or contingency of second causes taken away, but rather established.*
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> **Now this is precisely what the Molinist believes!** The Confession affirms God’s preordination of everything that comes to pass as well as the liberty and contingency of the creaturely will, so that God is not the author of sin. It is a tragedy that in rejecting middle knowledge Reformed divines have cut themselves off from the most perspicuous explanation of the coherence of this wonderful confession.
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William Lane Craig is Research Professor of Philosophy at Talbot School of Theology and Professor of Philosophy at Houston Baptist University.

The whole article is on [Reasonable Faith .org](https://www.reasonablefaith.org/writings/question-answer/molinism-vs.-calvinism/)

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(I do not personally subscribe to these arguments and proposals. I simply report the existence of the references and statements.)
TL;DR: Calvinists and Arminians disagree about whether man is able and/or free to choose God, Molinism is to do with God's knowledge and not salvation, so can fit with either.

Molinist here - Molinism isn't technically a view of soteriology (meaning to do with man's salvation), but is a view of God's knowledge, summed up pretty well by the gotquestions article referenced by Lesley. Molinism's two main points (or core doctrines) are:

1: God has Middle knowledge

2: Man, at least some of the time, has libertarian free will (although the precise definition is disputed, a reasonable interpretation of the term is 'the ability to do otherwise')

Arminianism and Calvinism, on the other hand, are directly opposing views that are to do with soteriology, not God's knowledge. Thus, you could be an Arminian Molinist or a Calvinist Molinist. The latter, however, is quite rare.

Calvinism is a very difficult doctrine to clearly define, but a working minimum of the system is summed up by the acronym TULIP. I won't go into a lengthy description of each of the letters (it's well documented in many places) but in summary Calvinism teaches that man, in his natural state, is completely unable to come to God (T) . God then 'elects' certain individuals whom He decides to save (U) and draws them to himself via irresistible grace (I) (literally irresistible, the elect person is unable to reject or refuse the grace). Additionally, Christ's atonement only covers and was only intended for these elect (L), and finally, the elect will never fall away or apostasize (P).

Arminianism is even harder to specifically define, but the gist is that although man would be unable to come to God alone, God's grace (prevenient grace) overcomes this state and enables all men to come to God and be saved, although it doesn't guarantee any will or force anyone. Christ's atonement covers any and all who come to Him, and is not limited. Beyond that, there are a lot of variations of Arminianism that I don't know as much as I should about.

It is worth noting that some (Many? Most?) Molinists hold to a soteriology which is similar to Arminianism but goes further in regards to God's providence and the election of individuals while maintaining free will, but that is beyond the scope of the question as it technically isn't Molinism proper.

Hope that helps