Hey, I have a friend of mine who played guitar for a little bit, but then stopped, but now she's wanting to learn again, and seems to have developed quite a passion and respect for the instrument. Her influences range from Stevie Ray Vaughan to Dream Theater to Children of Bodom, but her favorite artist is Steve Vai.

I think one of the main things in first learning guitar is finding a style that you think is fun and really fits what you're driving for, and of course as you progress, you'll likely want to advance your knowledge to separate corners, however I'm having a difficult time finding anything that may keep her interested, challenge her, as well as not discourage her to give up. Does anyone have any ideas?
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I can´t tell you, what songs u should practice with her or what kind of theory, cause i don´t know that girl, but i´m just in a situation like you She just started playin´guitar and cuz of that she´s often depressed and wants to give up, just keep her learning motivate her and tell her that she will get better very soon if she practices:P I think your idea about finding an own style is pretty good, it´s obvious every musician has to find HIS STYLE, but what about the other genres? A good guitarplayer should learn everything he can, it improves u a lot!
~so far
What is really important for the beginner to understand - and this is universal -is that:

You will suck at first

Plain and simple. You can not pick up the guitar and sound like Vai in one day. If you want to learn it as a hobby, then take your time and learn the fudamentals and you will get better.

However, if you are passionate about the instrument, then spend your time learning theoary, listening to other guitar players, and being patient with your self. There are lots of things to consider when learning guitar, but it really boils down to two concepts:

1. Head knowledge - learning music theory and how to apply it to the guitar
2. Mechanical knowledge - training your muscles, hands, fingers, etc. how to make the notes happen.

So know that you will suck at first, know that you will get better as you practice, and be patient with yourself.