Resources on Stone-Čech compactification

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I'm currently studying R.C. Walker's book on the subject which seems quite extensive and detailed. I've also been skimming through Hindman and Strauss's book Algebra in the Stone-Čech Compactification: Theory and Applications. Obviously they contain a large amount of citations to other books and research articles to have a glance at, but is there anything specific you would suggest?

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Could you try Gillman and Jerison's book: Ring of continuous functions. They explain the Stone-Čech compactification by continuous functions and filters (ultrafilter).