There are many major themes, but the ones most apparent to this eNotes educator are as follows:  perseverance and separation.

The theme of perseverance is mostly seen in the character of Rajkumar from the very beginning of the novel, where he is running as the lone survivor.  He eventually stands in the royal palace as it is being looted and falls in love with the handmaiden, Dolly.  Rajkumar also meets his mentor, Saya John.  It is Rajkumar who becomes rich (with the business help of Saya John) while the Burmese empire loses its riches. 

Yes, we who ruled the richest land in Asia are now reduced to this. . . . In our golden Burma, where no one ever went hungry and no one was too poor to write and read, all that will remain is destitution and ignorance, famine and despair.

Of course, as all of this is happening Rajkumar reunites with Dolly and the two get married. 

A second prominent theme is the usage of glass and mirrors as separation in The Glass Palace. This is especially true if we think about the setting of World War II and how it separates families. Even though the "glass palace" originally just means a hall in the royal home in Mandalay, it is Dolly who describes the walls and the mirrors and the glass and how they are memorable.  Rajkumar even speaks of Dolly in this way:

She was like the palace itself, a thing of glass, inside which you could see everything of which your imagination was capable.

Further, Dinu only sees live through his camera:  a protection from reality.  Again, a separation.

These two themes, perseverance and separation, are a good place to start if you are beginning an essay on the most major themes in this work of literature.