How does the Proof of Stake consensus algorithm work intimately?

Given all of the completely different implementations and discussions on Proof of Stake vs Proof of Work I discover myself a bit overwhelmed making an attempt to grasp the guts of this consensus algorithm. I even failed making an attempt wanting into the code repositories to determine it out.
My query is straightforward: can we define how the algorithm works and the way it achieves consensus extra intimately on this thread?
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