Impromptu is a Lisp language environment. More specifically a Scheme environment (a member of the Lisp family of languages). The Impromptu tutorials do not provide information on the Scheme language. For a brief introduction look here, here or here. For full texts look here, here and here.
If this is your first time using impromptu you can watch a VERY brief video introduction here
Making it go Bing
Write your first Impromptu program
Impromptu Basics
A brief run though some Impromptu basics. A must read!
Time
An introduction to timing in Impromptu. A must read!
Making A Noise
An introduction to making sound in Impromptu. A must read!
Making More Noise
A tutorial covering Audio Input, 3D Sound and Recording to Disk.
MIDI & OSC
An introduction to using MIDI and OSC in Impromptu.

An introductory tutorial movie covering basic image and live video manipulation.
Making Music
A series of tutorials looking at basic musical structures in Impromptu.
These are a work in progress and are likely to change regularly so check back often.
If you have any suggestions for improvements/things you'd like to see included let me know.
ObjC Bridge
Basic introduction to calling ObjC from Scheme.