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We construct two distinct yet related M-theory models that provide suitableframeworks for the study of knot invariants. We then focus on thefour-dimensional gauge theory that follows from appropriately compactifying oneof these M-theory models. We show that this theory has indeed all requiredproperties to host knots. Our analysis provides a unifying picture of thevarious recent works that attempt an understanding of knot invariants usingtechniques of four-dimensional physics.  This is a companion paper to arXiv:1608.05128, covering all but section 3.3.It presents a detailed mathematical derivation of the main results there, aswell as additional material. Among the new insights, those related tosupersymmetry and the topological twist are highlighted. This paper offers analternative, complementary formulation of the contentsin~\cite{Dasgupta:2016rhc}, but is self-contained and can be readindependently.

A companion to "Knot invariants and M-theory I'' [arXiv:1608.05128]: proofs and derivations