I will present two orders here, chronological order and the order in which they should be read.

#Order in which they should be read

This is *mostly* in chronological order, but it's ordered more in how they came out and how they will make the most sense.

**Percy  Jackson and the Olympians**

First comes *The Lighting Thief*.  
Then comes *The Sea of Monsters*.  
Then *The Titan's Curse*.  
The *The Battle of the Labyrinth*.  
Then *The Last Olympian*.

This is the original series; therefore, it should be read first.

Now you should read the short story collection *The Demigod Files*, as most of the stories take place during/after PJO.

**The Heroes of Olympus**  

First is *The Lost Hero*.  
Then *The Son of Neptune*.  
Then *The Mark of Athena*.  
Then *The House of Hades.*  
Then *The Blood of Olympus*.

After this would be a good time to read *The Demigod Diaries*, a collection of short stories.

That's the obvious part, as those are all in one universe. Now..

**The Kane Chronicles**  

First is *The Red Pyramid*.  
Then *The Throne of Fire*.  
Then *The Serpent's Shadow*.

Now, you should read the crossovers, as they only make sense if you've read KC and PJ:

First is *The Son of Sobek*.  
Then *The Staff of Serapis*.  
Then *The Crown of Ptolemy*.

Now, you should read *The Trials of Apollo* and *Magnus Chase and the Gods of Asgard* together, as they take place at the same time and may have spoilers if not read together.

First is *The Trials: The Hidden Oracle*.  
Then comes *Magnus: The Sword of Summer*.  
Then *Magnus: The Hammer of Thor*.  

The rest haven't come out yet.

#Chronological order

*The Demigod Diaries: The Diary of Luke Castellan*.  
*PJO: The Lighting Thief*.  
*PJO: The Sea of Monsters*.  
*PJO: The Battle of the Labyrinth*.
*Files: Percy Jackson and the Stolen Chariot*.  
*Files: Percy Jackson and the Bronze Dragon*.  
*Files: Percy Jackson and the Sword of Hades*.  
*PJO: The Last Olympian*.  
*Diaries: Percy Jackson and the Staff of Hermes*.  
*Kane: The Red Pyramid*.  
*Kane: The Throne of Fire*.  
*Kane: The Serpent's Shadow*.  
*HOO: The Lost Hero*.  
*Diaries: Leo Valdez and the Quest for Buford*.  
*HOO: The Son of Neptune*.  
*HOO: The Mark of Athena*.  
*HOO: The House of Hades*.  
*HOO: The Blood of Olympus.*  
*PJO/KC: The Son of Sobek.*  
*PJO/KC: The Staff of Serapis*.  
*PJO/KC: The Crown of Ptolemy*.  
*Magnus: The Sword of Summer.*  
*Trials: The Hidden Oracle*.  
*Magnus: The Hammer of Thor*.  

...And the rest of *The Trials of Apollo* and *Magnus Chase and the Gods of Asgard* haven't come out yet.

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All information in this answer came from my own reading of all of these books.

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The top order has been made depending on how the information has been given, such as the introduction of characters, plot points, etc. This ends up mostly being in the order that Rick Riordan released them in, with a few minor changes that take into account later books.