Function: local-set-key

Give KEY a local binding as COMMAND.
COMMAND is the command definition to use; usually it is
a symbol naming an interactively-callable function.
KEY is a key sequence; noninteractively, it is a string or vector
of characters or event types, and non-ASCII characters with codes
above 127 (such as ISO Latin-1) can be included if you use a vector.

The binding goes in the current buffer's local map,
which in most cases is shared with all other buffers in the same major mode.