As much as I hate to admit it, the Young Jedi Knights are not my creation.  Over the course of fourteen novels, writers Kevin J. Anderson and Rebecca Moesta chronicled the adventures of the next generation of Jedi.  Below I've got scans of all the novels' covers, and will soon add reviews of the books (as soon as I can re-read them, that is).
 
 

HEIRS OF THE FORCE                                                                                                       
SHADOW ACADEMY
THE LOST ONES
LIGHTSABERS
DARKEST KNIGHT 
JEDI UNDER SIEGE
SHARDS OF ALDERAAN
DIVERSITY ALLIANCE
DELUSIONS OF GRANDEUR
THE EMPEROR'S PLAGUE
JEDI BOUNTY
RETURN TO ORD MANTELL
TROUBLE ON CLOUD CITY
CRISIS AT CRYSTAL REEF