Anakin Solo is a human male Jedi Knight of the New Jedi Order, third child of Han Solo and Leia Organa Solo, and younger brother of Jacen and Jaina. He first appeared in Dark Apprentice (1994), the second novel of Kevin J. Anderson's Jedi Academy trilogy. He is Legends only: no canon counterpart exists, and the sequel trilogy's Ben Solo occupies a broadly similar structural slot with an entirely different story.
Hidden, then trained
He spent the first year of his life on Anoth, an isolated world fortified by Luke Skywalker and Admiral Ackbar to keep the Solo children out of Imperial reach, before joining his parents on Coruscant. At eleven he entered the Jedi Praxeum on Yavin 4, where his closest friend was Tahiri Veila.
The name problem, solved on the page
Naming a child after Darth Vader is a decision the Legends novels took seriously rather than waving through, and Anakin spends much of his adolescence being measured against a grandfather he never met. By the time of the Yuuzhan Vong War he had become the most decisive of the three Solo children — the one who acted while his brother theorised.
Myrkr
He led the strike team sent to end the voxyn, the creatures the Yuuzhan Vong had bred specifically to hunt Jedi, and died completing the mission. Star by Star (2001) by Troy Denning remains one of the most argued-about books in the entire Expanded Universe, and the argument is essentially this: was killing him the moment the New Jedi Order series proved it had stakes, or the moment it lost its best character to prove a point?
Where to read him
Anderson's Jedi Academy novels for the childhood, then the New Jedi Order sequence from Vector Prime to Star by Star. His death shapes everything Jacen does afterwards, up to and including the events of Legacy of the Force.