This page offers a list of Ancient Greek readers that you can download free of cost. You will need some basic previous exposure to Greek before being able to read even the most elementary ones, but they can provide invaluable experience in mastering the language.
I could not have compiled this list without help from several of you. Textkit and Google Books provide many of the PDF files, but E. Donnelly, Paul Nitz, and several others have pointed out links to those files making them easier to find. Thank you!
This page is a work in progress. As I find other readers that seem helpful and are available without cost, I will add them here.
The readings from Herodotus have been altered to make them conform to Attic usage: "... it seemed that a judicious selection of passages from Herodotus, when changed into Attic Greek, would put another book into the hands of the teacher."
This book includes readings from John's Gospel, short tales and anectotes, and fables.
Writing in the first half of the second century CE, Appian wrote in the common Greek of his time. This volume has the Greek text on even numbered pages and an English translation on the facing page.