Free BASIC Tutorials
Liberty BASIC Tutorials
This page has links to two sets of tutorials for Liberty BASIC - Beginning Programming and Game Programming.
This is the wikibook entry for QBasic. It is really more of a short QBasic tutorial than a book.
QBasic - Step By Step
QBasic tutorial covering fundamental aspects of the language, input and output, control structures, modules / sub procedures, looping, functions, arrays, array-type problems, records, and data files.