I don't really know how to write legalese, so I will say it in simple words:

You can use this library for any project, commercial and non-commercial,
open-source and closed-source. But if you modify the library, you must
redistribute the source for the modifications you did to it.
Not doing that constitutes an infringement of this license. 
You are not obliged to redistribute the source code of this library if it
was not modified at all by you or anyone related to you.

There is no advertising clause; you aren't obliged to mention this library
in any documentation of your work using it; however, it would be a nice gesture
if you did so.

These terms were written to not make people close this work which was released
for all to share. In fact, no use is otherwise restricted.

This license also applies to the following tools: 
bin2c, bmp2tim, getpsxiso, systemcnf

Some of the tools have a different license: 

for exefixup it is GPL version 2 or newer

Some of the libraries have a different license:

libfixmath is licensed under the MIT license
libmeidogte is licensed under version 2 of the Mozilla Public License

Some of the examples have a different license:

gtecube is licensed under version 2 of the Mozilla Public License

some of the other tools are derived from public sources with no clear licensing, but it
is assumed that they were public domain. In all cases, they are attributed
to their original authors.

The PSXSDK examples are not under this license and released directly into the Public Domain,
which means you can do everything with them and you do not have to preserve attribution.

-- Giuseppe Gatta