Power
Shakespeare is interested in royal power throughout his history plays. In "Richard II", he dramatizes two very different attitudes about kingship. According to Richard II and his followers, kings should inherit the crown from their fathers, and they have a right to rule because they are God's chosen representatives on earth.
Literary critics and historians point out that when Shakespeare was writing "Richard II", European ideas about power and monarchy were beginning shift from a religious attitude, like Richard's, to a more secular (non-religious) point of view
Gender
In "Richard II", the women tend to be associated with family, and they always, always put kinship bonds first. Yet even though the play's women are left out of politics, they serve an important function.
Identity
Many of the characters in this play get their identities from their titles, which is why they obsess so much about their names.
The same is true of Richard II, who has inherited the title of King of England from his father. When Richard loses his title, he experiences a major identity crisis.