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The Levine book can get into very complex theoretical discussion without any application, but to an advanced classical student this might be a more welcoming start. Here's some important stuff: Get a Real Book, try transcribing tunes off recordings, learn a ton of chords and use them in the context of the Real Book, practice licks in all 12 keys. Improvise over the changes in the Real Book. And Listen, especially live jazz at a club, but listen to jazz as much as possible.
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