Computability Logic - Wikipedia (free encyclopedia) article. - http://en.wikipedia.org/wiki/Computability_logic
What are Weak Arithmetics - Notes defining the subject. Available in HTML and PS formats. - http://www.univ-paris12.fr/lacl/jaf/html/wa.html
Logic System Interrelationships - Shows how a number of representative logics fit together. The interrelationships usually given as something of the form: System X is system Y plus the axiom Z. By John Halleck. - http://www.cc.utah.edu/~nahaj/logic/structures/
Infinitary Logic - Article in the Stanford Encyclopaedia of Philosophy by John L. Bell. Infinitary Logic is a branch of formal logic where finitary formulae are replaced by potentially infinitary mathematical entities. - http://plato.stanford.edu/entries/logic-infinitary/
Non Standard Logics - A comprehensive listing of flavours of non-standard logic with brief descriptions and references, compiled by Peter Suber. - http://www.earlham.edu/~peters/courses/logsys/nonstbib.htm