This was my GCSE textbook back in 2001, and I remember it fondly. It combines grammar lessons with short translation exercises which introduce Greek literature and culture. By the end of the book it is possible to read extracts from literature and philosophy texts. It went well beyond the language level required for GCSE, and, thanks to my teacher as well, I can recall a great deal nine years later. I found Thrasymachus to be an excellent introduction to Ancient Greek.
Customers intending to teach themselves Greek without the help of a tutor might consider buying a grammar book as well, such as the Oxford Grammar of Classical Greek. Although grammar points are clearly explained in Thrasymachus, it is always wise to read another author's explanation.
Customers whose interest in Greek is less serious might prefer Peter Jones's "Learn Ancient Greek". This has amusing cartoons and clear explanations of grammar. I used it to revise for my GCSE, and I found it very entertaining. However, the vocabulary required for the translation exercises does not build up as logically as in Thrasymachus: that is, a great deal of new vocabulary is introduced in each exercise, and this can be daunting.
For those wishing to study Greek seriously, it is highly advisable to find a tutor. No textbook is perfect, and the support of a more experienced scholar is invaluable and can overcome even the most ill-conceived course book.