Here is an ultrafinitist manifesto I have co-written a few years ago:

* Mirco A. Mannucci, Rose M. Cherubin, _Model Theory of Ultrafinitism I: Fuzzy Initial Segments of Arithmetics_, https://arxiv.org/abs/cs/0611100

It is absolutely not a finished paper (there are a few inaccuracies, and many parts are sloppy), but it contains a brief history of ultrafinitistic ideas from the early greeks all the way to present time, a number of refs,  as well as a sketch of a programme towards a model theory and a proof theory of ultrafinitistic mathematics. 

You may also want to google the  FOM list  on "ultrafinitism", there are a few posts by Podnieks, Sazonov, myself, and a few others pro and contra ultrafinitism.