Kent and Gloucester are in King Lear's court, discussing Lear's plan to give up his power and divide it among his daughters. Gloucester introduces Kent to his illegitimate son, Edmund, who is standing nearby. Gloucester says that, although Edmund is a "knave" (1.1.21) born out of wedlock, Gloucester loves him no less than the other "son" he has "by order of law" (1.1.19) (i.e., Edgar).
Gloucester's words to Kent show that he values his bond with his illegitimate son, despite the fact that a "natural" (i.e. biological) rather than a social or legal order connects them. This conversation looks ahead to the dismembering of the British kingdom by Lear.
Lear enters with Albany, Cornwall, Goneril, Regan, Cordelia, and their attendants. Having sent Gloucester to fetch Cordelia's suitors, the lords of France and Burgundy, Lear announces that he has divided his kingdom into three parts. He intends to "shake all cares and business from his age,/ Conferring them on younger strengths" so that he can "unburdened crawl toward death" (1.1.41-2).
Ironically, Lear's authority as king, as the head of a political order, enables him to make the decision that will produce grave disorder. By using the word "crawl" to describe his progress toward death, Lear describes the aging human without his former authority as an animal.
Next, Lear calls upon each of his daughters to state how much she loves him. First, Goneril insists that she loves her father "dearer than eyesight, space, and liberty" (1.1.61); Lear awards her one third of his kingdom, accordingly. Then, Regan claims that she loves her father even more than Goneril does; she is an "enemy to all other joys" but his "dear Highness' love" (1.1.80-4). Lear grants her a third, in turn.
The ceremony Lear has devised to make himself feel good also reinforces the plays theme of the connections between the "public" authority of Lear as a king and his "private" authority over his daughters as a father.
While her sisters speak, Cordelia grows nervous, knowing that she would prefer to "love, and be silent" (1.1.68) than to make such a public declaration of her love for her father. And, indeed, when her turn comes to speak, Cordelia can answer only "Nothing, my lord" (1.1.96). Lear presses her to give another answer, but she insists that she loves him "according to [her] bond, no more, no less" (1.1.102).
Enraged by this refusal to play along, and vowing by "all the operation of the orbs" (1.1.124), Lear renounces his "paternal care" of Cordelia forever (1.1.127). When Kent attempts to intercede on Cordelia's behalf, Lear reiterates: "here I give/ her father's heart from her" (1.1.141-2). He states that he will from now on alternate months living with his two other daughters, keeping only 100 knights on reserve to be his followers. When Kent continues to counsel him against such a rash decision, Lear banishes him on pain of death: "out of my sight!" (1.1.179). Having consoled Cordelia, and exhorted Goneril and Regan to live up to their declarations of love, Kent departs.
Lear invokes the heavens as a symbol of order and justice for the first of many times throughout the play. Kent, meanwhile, shows a personal devotion to Lear that is so strong that he is willing to step outside of the usual political order (i.e., the rules of the court) in order to try to protext his king. More insightful than Lear, Kent knows that dividing the kingdom is a bad idea; he also sees Goneril and Regan for the opportunists they are.
Gloucester returns with France and Burgundy. Lear addresses Burgundy first, telling him that Cordelia has been disowned. Cordelia interrupts, begging her father to explain that she has not done anything wrong: her only sin is to lack a "still-soliciting eye and such a tongue" (1.1.266) as her sisters. Burgundy asks, won't Lear give the dowry he proposed? Lear replies that he will give "nothing" (1.1.283). Then, Burgundy apologizes, he cannot marry Cordelia. France, however, says that the neglect of the gods has only increased his love: he pronounces Cordelia his wife and queen. Lear accepts and exits with his attendants.
Cordelia then takes leave of Goneril and Regan, saying she knows their faults, but hopes that they will live up to the love they have declared. Cordelia and France leave. Left alone, Goneril observes that Lear's old age is "full of changes" (334) and that he showed "poor judgment" (337) casting off Cordelia. Regan agrees the "infirmity of his age" (339) is to blame for his error. Goneril says that in these "infirm and choleric years" (345) they cannot permit their father to exercise any real authority.
Cruelly criticizing their father's senility, the sisters show their true colors for the first time, foreshadowing all the abuses that they will soon wreak on him due to his age. Like Kent, they also describe what Lear has done as an error. But they, unlike Kent, plan to take advantage of it, and show more interest in power than in the love they owe their father simply because he is their father.