(1.) Groundless-ness, this video essay highlights the anglicized translation 'All things are Possible", but the more literal translation Apotheosis of Groundless-ness is worth examining. For Shestov if you keep pulling on the thread of inquiry and skepticism - relentlessly without settling for expedient, pragmatic or comfortable answers - then you are left metaphorically floating in a foundation-less void. I'm not well versed in the categorization but this might be a form of epistemic nihilism??? Shestov believes that all authentic philosophy leads to this place of groundless-ness.

(2.) Despair, Shestov is sometimes called the philosopher of despair. I think Shestov's concept of despair is formed at both a emotional and existential level. We know that Shestov lost his son in the first world war and that this loss profoundly impacted him. Also in his letters he often refers to an early experience in his young adult life that may have lead to what we might today understand as a mental breakdown / serious depressive episode.
On the existential side of things, despair is engendered from this place of groundless-ness, from the human need for answers and explanations and the total lack of them in the world. Despair arises from the complete proliferation of unanswerable mystery that surround us. One of the most famous engagements with Shestov is in Albert Camus' "The Myth of Sisyphus" specifically Camus' chapter on the absurd, and philosophical suicide.

(3.) Truth and Freedom. In what is sometime considered his magnum opus "Athens and Jerusalem" Shestov argues that Truths are always constraints. To admit a truth is to admit a limitation on what is possible, and therefore truth and freedom will always be antithetical. I think this is the most contentious part of Shestov's philosophy and I personally still don't know what to make of it. I think Shestov advocates for an extreme fideist position where we should choose freedom/faith - a world where everything is possible - over a world of logic, constraint and truth.

Just as there is debate in Nietzsche interpretation regarding whether he is better understood as a existentialist or proto-postmodernist i think a similar questions could be asked of Shestov. Particularly in regards to Truth Regimes and Logocentrism, understanding the ways truth can be used as an oppressive and hegemonic tool. Off the top of my head I know Shestov had a big influence on Deluze and Guattari.

(4.) Faith, I think it was Cioran who said that Shestov was the last of his generation able to realize himself spiritually. This certainly resonates for those who find his extreme fideism hard to swallow. Looking at other religious existentialists helps contextualize his philosophy, I.e. Nikolai Berdyaev, Soren Kierkegaard, Karl Jaspers, and Gabriel Marcel. I think one area where the video from this post falls short, is that Shestov's belief that all things are possible is very much a religious belief inspired by his theology. Namely that God is a being to whom all things are possible, and it is only because of God that all things are possible...