Eragon → Eldest → Brisingr → Inheritance. Murtagh (2023) is a standalone sequel set after Inheritance — read it last.
Yes, the original four-book cycle is complete. Paolini returned with Murtagh (2023), a standalone sequel focusing on a supporting character from the main series.
Paolini began writing Eragon at age 15, when the book was self-published. It was picked up by Knopf and professionally published when he was 17–18, making him one of the youngest traditionally published debut novelists.