What is the basic theme of The Trials of Apollo?

The basic theme of Rick Riordan's series The Trials of Apollo is the importance of empathy. The Trials of Apollo is a pentalogy, or series of five books. As of September 2019, the series has not yet been finished. The books relate to the god Apollo undertaking five tasks in human form in order to have his divinity restored after he has angered his father, Zeus.
As a god, Apollo did not have empathy for the humans he considered below him, or even for his own half-mortal children. Zeus's punishment—turning Apollo human—forces him to understand the lived experience of those who are not gods. A large part of Apollo's growth in the books of the series that have been published (The Hidden Oracle, The Dark Prophecy, and The Burning Maze) lies in his revisiting individuals he has interacted with in the past and recognizing their struggles and his responsibility to them. This recognition and increase in responsibility cause Apollo to become a more empathetic.

The basic theme of the The Trials of Apollo series is growth and acceptance. Apollo has to grow as a human to regain his godhood and accept the limitations and quests placed before him.
When Zeus casts Apollo to Earth as punishment for his misdeed, Apollo is aghast. He doesn't want to be a weak human; he wants to be a God again. Part of being able to regain what he's lost, however, is him growing as a being to both accept his situation and accept what he has to do to change it.
One way that Apollo changes and grows is in his relationships with other people. He didn't have to worry about friends when he was a God. As a teenage boy, he has to rely on other people and be the kind of person others -- like Meg -- are willing to work with. As he grows to be a better person and accepts the quests ahead of him, Apollo works to return to Olympus.

The basic theme in Rick Riordan's The Trials of Apollo concerns the change in perspective that the main character undergoes. The novel begins as the god Apollo finds himself sent down from Olympus to Earth in the body of a teenager as a punishment from his father, Zeus. He has to accomplish several missions in order to return back "home" as a god. Apollo is selfish, narcissistic (though not unkind, sometimes), and ill-equipped to deal with the limitations of a human (and mortal!) body and mind. Much like a person in good health might find it difficult to relate to someone with a disability, Apollo the god cannot relate to mortals or demigods and the challenges they face. Lester, as Apollo is now called, spends a lot of his time processing the predicament he is in and comparing his current capabilities to the godly powers he used to have. Now he has to give up his comfort and risk his life for someone else—something he used to expect the demigods, including his own children, to do for his benefit. Eventually, though with great difficulty, he develops empathy for others, and his relationships are no longer guided by pure self-love, all because he was forced to step into someone else's shoes. Seeing the world through the eyes of Lester changes Apollo's perspective—and we, the readers, can appreciate the lessons he has learned the hard way.