These are the core novels (i.e. the one you should not skip) that provide the backbone to the entire book series. The books are traditionally broken into "eras", each era covering the adventures of the main heroes (and later on their descendents) over the centuries in the world of Krynn. They are listed here in suggested reading order (that is also the publication and chronological order).
The Dragonlance Chronicles novels were based on a series of Dungeons & Dragons (D&D) game modules. The Chronicles trilogy came about because the designers wanted novels to tell the story of the game world they were creating, something to which TSR, Inc. (TSR) agreed only reluctantly.... they did not know that this trilogy was soon to become a New York Times bestseller!
Dragonlance Legends is the second trilogy of fantasy novels written by Margaret Weis and Tracy Hickman, which take place in the Dragonlance setting. This series is the sequel to the Dragonlance Chronicles, and has two major story arcs: Raistlin Majere's aspirations to godhood, and his twin Caramon Majere's attempts to stop him; and the machinations of Kitiara uth Matar, the twins' half-sister, and her attack on the city of Palanthas as part of the Blue Lady's War.
The Second Generation
Short sequels stories set after the event of the previous two trilogies. "The Second Generation" refers to the nature of the stories, being that they are the "Second Generation" of heroes, the children of the Heroes of the Lance.
Dragons of a New Age
A decade after the last "core" novel was published, dragonlance introduce a new campaign settings backed by a new series of books, for the first time not authored by Weis or Hickman. They are set during the Age of Mortal, when Gods and magic are gone. The feel is very different from the classic magic-heavy dragonlance settings, and the books were not as successful as the previous "core" ones. They are excelent though.
The Dhamon Saga
Dhamon Grimwulf, once a Hero of the Heart, has sunk into a bitter life of crime and squalor. Now, as the great dragon overlords of the Fifth Age coldly plot to strengthen their rule and to destroy their enemies, he must somehow find the will to redeem himself. But perhaps it is too late.
The War of Souls
The world of Krynn became a very different place with the disappearance of the gods. Dragons, much larger and more malicious than any native to Krynn, appeared and claimed much of the continent of Ansalon, calling themselves Dragon Overlords. Most of the native dragons are either dead or enslaved. The metallic dragons have disappeared. With the loss of the gods comes the loss of magic, and the Wizards' Conclave had been disbanded years ago. Although sorcery, discovered by Palin Majere, was adopted, it is slowly fading for reasons unknown. Everyone, including the Dragon Overlords, experiences the effect. The Knights of Takhisis, with the loss of their Queen, became the Knights of Neraka, a somewhat less honorable outfit than their predecessors, led by Lord of the Night Morham Targonne. Goldmoon, one of the few remaining Heroes of the Lance, has established the Citadel of Light on the island of Schallsea. In the elven realm of Qualinesti, Gilthas, the "puppet king", rules only in title, while the nation is truly run by the occupying Knights of Neraka. Their cousins, the Silvanesti, have banished their heir, Silvanoshei, his mother, and his father. With the gods gone, the time period, fittingly, is known as the "Age of Mortals".
The Dark Disciple
The book takes up where the War of Souls left off. This trilogy will explore the Chaos that is post-war Krynn
These books and subseries provide background on some of the characters, location, and historical moment that appear or are mentioned in the core novel. Some of them are extremelly entrateining and as good as the core novels.
The Raistlin Chronicles
This duology follows the two brother Mejere from childhood to the beginning of the Chronicle trilogy saga.
The Lost Chronicles
Decades after the original Chronicle trilogy was published, the authors decided to write another trilogy telling the untold stories of the original trilogy. The original trilogy had some temporal gaps between each books, and these books tell what happened then. While not as good as the original trilogy, I loved meeting my childhood heroes again. If you loved dragonlance as a kid, you cannot skip these books. If you want to avoid spoilers, read these books AFTER the Chronicle AND legend Trilogies.
A stand alone duology following a group of draconians after the end of the War of the Lance. In my opinion, this is one of the best Dragonlance subseries.
This is one of the best dragonlance series, but it is not an "official" one: the books of the series are not collected in a single official Dragonlance trilogy, they are spread across many, but they feature the same characters and a quite intriguing plot line that increases in complexity and scope over the years. The series is independent from the other dragonlance books, i.e. it could be read as a stand-alone series. Still, reading the main "dragonlance chronicles" trilogy may provide some useful background.