Faster LIKE

I have an image database with keywords assigned to each record
in the field "keywords" and often do:

select * from images where keywords like 'dog';

which works great with a small database, but slows down quickly
with a large database.

since the "keywords" field can have multiple entries, such as
'dog mammals fuzzy small' I was considering creating a separate
keywords table where each word was an individual row and could
therefore be indexed and fast.

however, in the above example, I would like to match on "mammal"
also (i.e., no "s" on the end) or any substring within the field, so
the separate table does not do it either.

This has to be a common thing. Are there any good solutions or
research out there to solve this problem? Thanks.