Calvinism is a system of thought that has been embraced by many since the time of the Reformation. And some of its philosophical concepts go back all the way to Augustine.
The first main concept is a form of soft determinism called “compatibilism.” Simply put, compatibilism teaches that God unilaterally determines every thought, word, and deed of every creature in all of history, and yet this determinism is deemed to be compatible with the idea that each creature is still morally responsible for their thoughts, words, and deeds.
The acronym TULIP sums up the 5 points of Calvinism’s idea about the nature of salvation.
T stands for Total Depravity. This doctrine teaches that each person is so corrupt from birth that they could never respond in repentance or faith towards God and Christ even if the Holy Spirit comes to the person and convicts them of their sin.
U stands for Unconditional Election. This doctrine teaches that God unilaterally chose before the world began whom He would give the gift of faith and repentance to so they could be saved. And it further teaches that He left the rest of mankind without the ability to repent or believe so that He could show His wrath on them forever.
L stands for Limited Atonement. This doctrine teaches that Jesus paid the penalty for specific sinners and their sins. He only died for those whom God unconditionally elected for His own purposes.
I stands for Irresistible Grace. This doctrine teaches that God unilaterally causes a person to be born again, and made into a new creature in Christ, without the will of the sinner being involved. And then, since the person is made new, he then naturally repents and believes unto justification.
P stands for Perseverance of the Saints. This doctrine teaches that God will make sure that those whom He saves, will continue in holiness until the end of their lives and thus inherit eternal life.
The last main perspective in the Calvinistic philosophy is Covenant Theology. This paradigm teaches that God has saved people in history, both in the Old and New Testaments through faith. And that in the Old Testament they had different signs, but the same salvation as those in the New. For example, in the Old Testament, male children were made part of God’s people by being circumcised as babies. In the same way, people are now made part of God’s people through baptism as babies. (Note: Baptist Calvinists have adjusted their view on Covenant Theology for obvious reasons)
Here is a short video on this topic:
Kingdom Theology 