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You can learn a decent amount of Japanese on your own... However, you'll never become fluent without a tutor or a class. There are many nuances about the Japanese language that you just can't learn from a book. Even with intensive classes, it can take several years to become fluent in Japanese -- imagine how long it would take to learn all of it by yourself.

I will say that I too have used the Genki textbooks for my classes a few years back. They're pretty good books, and I liked them, but they're only the beginning - there's only two books, and no more. It may take over a year or two just to master and memorize everything in these books.