The play begins with King Lear taking the decision to abdicate the throne and divide his kingdom among his three daughters: Goneril, Regan and Cordelia. The eldest two are already married, while Cordelia is much sought after as a bride, partly because she is her father’s favourite. In a fit of senile vanity, he suggests a contest — each daughter shall be accorded lands according to how much they demonstrate their love for him in speech. But the plan misfires. Cordelia refuses to outdo the flattery of her elder sisters, as she feels it would only cheapen her true feelings to flatter him purely for profit. Lear, in a fit of pique, divides her share of the kingdom between Goneril and Regan, and Cordelia is banished. The King of France however marries her, even after she has been disinherited, since he sees value in her honesty, or perhaps a casus belli to subsequently invade England.
Soon after Lear abdicates the throne, he finds that Goneril and Regan’s feelings for him have turned cold, and arguments ensue. The Earl of Kent, who has spoken up for Cordelia and been banished for his pains, returns disguised as the servant Caius, who will “eat no fish” (that is to say, he is a Protestant), in order to protect the king, to whom he remains loyal. Meanwhile, Goneril and Regan fall out with one another over their attraction to Edmund, the bastard son of the Earl of Gloucester — and are forced to deal with an army from France, led by Cordelia, sent to restore Lear to his throne. A cataclysmic war is fought.
The subplot involves the Earl of Gloucester and his two sons, the good Edgar and the evil Edmund. Edmund concocts false stories about his legitimate half-brother, and Edgar is forced into exile, affecting lunacy. Edmund engages in liaisons with Goneril and Regan. Gloucester is confronted by Regan’s husband, the Duke of Cornwall, but is saved from death by several of Cornwall’s servants, who object to the duke’s treatment of Lear; one of the servants wounds the duke (but is killed by Regan), who throws Gloucester into the storm in order for him to, “smell his way to Dover” after plucking out his eyes. Cornwall dies of his wound shortly thereafter. The storm scene is where Lear exclaims how he is “a man more sinned against than sinning”.
Edgar, still under the guise of a homeless lunatic, finds Gloucester out in the storm. The earl asks him whether he knows the way to Dover, to which Edgar replies that he will lead him. Edgar, whose voice Gloucester fails to recognise, is shaken by encountering his blinded father and his guise is put to the test.
Lear appears in Dover, wandering about raving and talking to mice. Gloucester attempts to throw himself from a cliff, but is deceived by Edgar in order to save him and comes off safely, encountering the king shortly after. Lear and Cordelia are briefly reunited and reconciled before the battle between Britain and France. After the French lose, Lear is content at the thought of living in prison with Cordelia, but Edmund gives orders for them to be executed.
Edgar, in disguise, then fights Edmund, fatally wounding him. On seeing this, Goneril, who has already poisoned Regan out of jealousy, kills herself. Edgar reveals himself to Edmund and tells him that Gloucester has just died. On hearing this, and of Goneril and Regan’s deaths, Edmund tells Edgar of his order to have Lear and Cordelia murdered and gives orders for them to be reprieved - perhaps his one act of goodness in the entire play.
Unfortunately, the reprieve comes too late. Lear appears on stage with Cordelia’s dead body in his arms, having killed the servant who hanged her, then dies himself.
Besides the subplot involving the Earl of Gloucester and his sons, the principal innovation Shakespeare made to this story was the death of Cordelia and Lear at the end. During the eighteenth and nineteenth centuries, this tragic ending was much criticised, and alternative versions were written and performed, in which the leading characters survived and Edgar and Cordelia were married.
[Source Encyclopaedia Britannica]