How can I stop an invasion of six-legged creatures?

I don’t know why, but I am experiencing an ant invasion. I go in the bedroom and they are marching across my bedroom wall. I leave anything in the kitchen and they take over the bench, the sink or anywhere else they can get.

I don’t really like killing insects, but I really do want these unwanted visitors to leave. Does anyone have any tried and tested ant eradication suggestions?