I would like to explore the world of improvisation, but I am a little lost. I know the basics about theory, I have notion of intervals, scales and chords, but I am willing to develop myself with ear training and improvisation. What are the best books? (I don`t have a teacher)
There are a lot of technical things you can learn, i.e. theory, scales, harmonies, etc. But I think the real way to improvisation is to sing and then try to play what you sung. In other words, if you play a lot of scales and things, you may find yourself having your fingers dictate your music from memory and rote rather than your inner music dictating where your fingers will go. I think it's great to listen, listen, listen to various music and styles, some guitar and other stringed instruments, as well as other instruments and singers and incorporate that with your technical learning. Basically, sing the licks, melodies you want to play. Then play with those licks, try to vary them, try to take snippets of them and branch off into other things. In time, you'll find the music almost improvising itself. Then play these things or see how close you can with your instrument.
I have a site on improvisation and more on that approach if you are interested. There's a section on make your own improvs.
While there are a number of reference books about guitar improvisation there is no substitute for experience. Such a reference library might include the following books:
Hal Leonard Improvising Lead Guitar Book and CD
Mel Bay's Complete Book of Guitar Improvisation (Mb93278)
Berklee Press Jazz Improvisation for Guitar Book/CD
The Big Book of Jazz Guitar Improvisation: Tools and Inspiration for Creative Soloing, Book & CD
...costing about $25 each.
Before you spend any money on these books you might want to read about how one player's experience with using such books shaped these conclusions:
I am a novice guitarist for sure and in no way consider myself an authoritative voice on this subject however I do have some experience extending many years that might offer some insight.
Improvisation for me is the fusion of previous musical experiences and a new experience. That is to say the more familiar you are with the fretboard, scales, modes, and how to modulate will lend itself well to taking a leap into blending things in a new way. With that said, here are the 5 keys to improvisation:
1) mastering your instrument
2) using your imagination
3) performing with others aka jam sessions, especially jazz where everyone takes a solo
4) experimentation and exploration as a way to shake up your mind and open new doors
5) understanding how all of the above work together to further your abilities to improvise
Finally consider how improvisation is used in other forms: painting, cooking, acting, poetry, story telling, etc. Study how other artists have used improvisation as a way to leap ahead. Consider how such art forms as cubism, surrealism, aleatoric music, abstract expressionism, modernism, and jazz relied on improvisation to render new forms.