Analysis and criticism of King Lear over the centuries has been extensive.
What we know of Shakespeare's wide reading and powers of assimilation seems to show that he made use of all kinds of material, absorbing contradictory viewpoints, positive and negative, religious and secular, as if to ensure that King Lear would offer no single controlling perspective, but be open to, indeed demand, multiple interpretations.R. A. Foakes 
John F. Danby, in his Shakespeare's Doctrine of Nature – A Study of King Lear (1949), argues that Lear dramatizes, among other things, the current meanings of "Nature". The words "nature," "natural" and "unnatural" occur over forty times in the play, reflecting a debate in Shakespeare's time about what nature really was like; this debate pervades the play and finds symbolic expression in Lear's changing attitude to Thunder. There are two strongly contrasting views of human nature in the play: that of the Lear party (Lear, Gloucester, Albany, Kent), exemplifying the philosophy of Bacon and Hooker, and that of the Edmund party (Edmund, Cornwall, Goneril, Regan), akin to the views later formulated by Hobbes. Along with the two views of Nature, Lear contains two views of Reason, brought out in Gloucester and Edmund's speeches on astrology (1.2). The rationality of the Edmund party is one with which a modern audience more readily identifies. But the Edmund party carries bold rationalism to such extremes that it becomes madness: a madness-in-reason, the ironic counterpart of Lear's "reason in madness" (IV.6.190) and the Fool's wisdom-in-folly. This betrayal of reason lies behind the play's later emphasis on feeling.
The two Natures and the two Reasons imply two societies. Edmund is the New Man, a member of an age of competition, suspicion, glory, in contrast with the older society which has come down from the Middle Ages, with its belief in co-operation, reasonable decency, and respect for the whole as greater than the part. King Lear is thus an allegory. The older society, that of the medieval vision, with its doting king, falls into error, and is threatened by the new Machiavellianism; it is regenerated and saved by a vision of a new order, embodied in the king's rejected daughter. Cordelia, in the allegorical scheme, is threefold: a person; an ethical principle (love); and a community. Nevertheless, Shakespeare's understanding of the New Man is so extensive as to amount almost to sympathy. Edmund is the last great expression in Shakespeare of that side of Renaissance individualism – the energy, the emancipation, the courage – which has made a positive contribution to the heritage of the West. "He embodies something vital which a final synthesis must reaffirm. But he makes an absolute claim which Shakespeare will not support. It is right for man to feel, as Edmund does, that society exists for man, not man for society. It is not right to assert the kind of man Edmund would erect to this supremacy."
The play offers an alternative to the feudal-Machiavellian polarity, an alternative foreshadowed in France's speech (I.1.245–256), in Lear and Gloucester's prayers (III.4. 28–36; IV.1.61–66), and in the figure of Cordelia. Until the decent society is achieved, we are meant to take as role-model (though qualified by Shakespearean ironies) Edgar, "the machiavel of goodness", endurance, courage and "ripeness".
Since there are no literal mothers in King Lear, Coppélia Kahn provides a psychoanalytic interpretation of the "maternal subtext" found in the play. According to Kahn, Lear in his old age regresses to an infantile disposition, and now seeks for a love that is normally satisfied by a mothering woman. Her characterisation of Lear is that of a child being mothered, but without real mothers, his children become the daughter-mother figures. Lear's contest of love serves as the binding agreement; his daughters will get their inheritance provided they care for him, especially Cordelia, on whose "kind nursery" he will greatly depend. Her refusal to love him as more than a father is often interpreted as a resistance from incest, but Kahn also inserts the image of a rejecting mother. The situation is now a reversal of parent-child roles, in which Lear's madness is essentially a childlike rage from being deprived of maternal care. Even when Lear and Cordelia are captured together, this madness persists as Lear envisions a nursery in prison, where Cordelia's sole existence is for him. However, it is Cordelia's death that ultimately ends his fantasy of a daughter-mother, as the play ends with only male characters left.
Sigmund Freud asserted that Cordelia symbolises Death. Therefore, when the play begins with Lear rejecting his daughter, it can be interpreted as him rejecting death; Lear is unwilling to face the finitude of his being. The play's poignant ending scene, wherein Lear carries the body of his beloved Cordelia, was of great importance to Freud. In this scene, she causes in Lear a realisation of his finitude, or as Freud put it, she causes him to "make friends with the necessity of dying". It is logical to infer that Shakespeare had special intentions with Cordelia's death, as he was the only writer to have Cordelia killed (in the version by the Nahum Tate, she continues to live happily, and in Holinshed's, she restores her father and succeeds him).
Alternatively, an analysis based on Adlerian theory suggests that the King's contest among his daughters in Act one has more to do with his control over the unmarried Cordelia.
In his study of the character-portrayal of Edmund, Harold Bloom refers to him as "Shakespeare's most original character". "As Hazlitt pointed out," writes Bloom, "Edmund does not share in the hypocrisy of Goneril and Regan: his Machiavellianism is absolutely pure, and lacks an Oedipal motive. Freud's vision of family romances simply does not apply to Edmund. Iago is free to reinvent himself every minute, yet Iago has strong passions, however negative. Edmund has no passions whatsoever; he has never loved anyone, and he never will. In that respect, he is Shakespeare's most original character."
Critics are divided on the question of whether or not King Lear represents an affirmation of Christian doctrine. Among those who argue that Lear is redeemed in the Christian sense through suffering are A. C. Bradley and John Reibetanz, who has written: "through his sufferings, Lear has won an enlightened soul". Other critics who find no evidence of redemption and emphasise the horrors of the final act include John Holloway and Marvin Rosenberg. William R. Elton stresses the pre-Christian setting of the play, writing that, "Lear fulfills the criteria for pagan behavior in life," falling "into total blasphemy at the moment of his irredeemable loss".
In the first edition of the Grimms Kinder und Hausmärchen, the Grimms made a note in the Anhang (appendix) entry to No. 71 Princess Mouse-skin: "as the father here, so asks King Lear his daughter". The English translation of this story by Oliver Loo begins as follows: "A king had three daughters; thereon he wanted to know, which loved him most, let them come in front of him and asked them. The eldest spoke, she loved him more, than the whole kingdom; the second, more than all the precious stones and pearls in the world; but the third said, she loved him more than salt. The king was so upset, that she compared her love of him with such a small thing, gave her to a servant and commanded, he should take her into the forest and kill her."