Cropping raster layer using QGIS?

The Raster|Extraction|Clipper tool will help you to do this.

You can open the tool and then click and drag in the raster image to select the area you want to export as a new raster (Clipping mode: Extent), and then refine the exact coordinates in the Extent fields (if necessary).

Probably no way to do contours on only a selection of a raster; clip it this way first!

I think the previous answer needs to fill extent by hand, since a better, automatic solution is:

go to Processing toolbox and call "Crop to data" SAGA (Raster Tools) process.