Inheritance
The central conflict of King Lear revolves around the concept of inheritance. At the beginning of the play, Lear aims to test his three daughters' loyalty before gifting them their portion of his land. The prospect of this inheritance is what fuels the boorish behavior of Goneril and Regan, but it is also Lear's selfish way of wielding continued power over his three daughters. In many ways, the inheritance proposed at the beginning of the play represents Lear's last form of control as a ruler.
Order
At the beginning of the play, Lear is represented as a controlling authority figure. Having divided his land into three parts to be designated to each of his three daughters, Lear wields power over his children in a way that spurs competition between them. Lear's bizarre and self-aggrandizing test of his daughters' affections can be interpreted as one of the ways he combats the reality of his age: becoming weaker physically, Lear attempts to hold onto power and control by orchestrating a division of his lands before his death.
Chaos
Predictably, Lear's plan in Act One to impose order on his three daughters quickly disintegrates, in part because of Lear's own ego. Once Cordelia confesses her true, but misunderstood, loyalty to her father, Lear strips Cordelia of her inheritance altogether. This decision is what leads to Goneril and Regan's betrayal of Lear and the general breakdown of order in the play. His decision also catalyzes his own descent into madness and his ultimate demise.
Aging
Modern productions of King Lear almost always present Lear as noticeably decrepit, and tend to emphasize his aging body as the play progresses. This focus on aging is central to the conflicts and plots of the play, as Lear's age inspires both anxiety in himself and greediness in Goneril and Regan, who eventually turn on him for their own gain. Ironically, in Lear's attempt to maintain political and familial control despite his physical decline, he ends up pushing himself further into senility.
Madness
Many describe Lear's character trajectory within the play as a fall from stern authority figure to madman. Indeed, his episode at Dover Beach is often used as evidence for Lear's lost grasp on reality. However, it is important to note that in his seemingly declining state, Lear gains insight into his mistakes as both a ruler and a father. Lear's "mad" ramblings even come to resemble remarks of the fool, who is often considered, ironically, the wisest character in the play.
Sight and Blindness
The play is rife with imagery of light, seeing, blindness, and darkness. This focus mirrors the figurative "blindness" that both Lear and Gloucester are guilty of, as they severely misjudge their children in the beginning of the play and experience the consequences thereafter. Lear, ironically, gains figurative "sight" as he becomes more mad, while Gloucester is literally blinded by Regan and Cornwall in Act Three. However, just like Lear, Gloucester gains a form of "sight" only after literally losing his ability to see, emphasizing how truth often only appears to one in retrospect.
Justice and Nihilism
King Lear is often discussed as a play that is obsessed with justice and punishment: Lear strips Cordelia of her inheritance after misinterpreting her declaration of love, Gloucester is blinded for potentially committing treason, Lear's mistake leads him to go mad, and Goneril and Regan's brutish behavior ultimately ends in their murder-suicide. As a tragedy, the sheer number of deaths and brutal punishments is not out of the ordinary for the genre. However, the play suggests that these deaths derived from misunderstanding, lack of communication, and uncertainty more generally. As such, many argue that King Lear presents a nihilistic view of the world, in which all values are inherently meaningless, including the concept of justice.