Undeterred means something tried to stop you and did not. It is a small word carrying a whole story: there was an obstacle, a warning, a bad result, a discouraging piece of news — and the person kept going anyway. That is why it so often appears with "by": undeterred by the rain, undeterred by the cost, undeterred by two earlier failures. It can also stand alone at the front of a sentence — "Undeterred, she applied again" — which is a favourite of newspaper writers because it packs the setback and the persistence into one word. The feeling is admiring, usually: brave, stubborn in a good way. But it can be dry or even a little mocking, depending on what the person insists on doing — "undeterred by the smell, he ordered a second one". Notice that it needs a discouraging thing nearby to make sense; you cannot be undeterred out of nowhere. It is a written, slightly formal word. In talk people say "he didn't let it stop him" or "she carried on anyway".