How can I connect two edge loops with different numbers of vertices? I can't use the F function because the number of vertices in each circle is not same. 
The big one has 48 and the small one has 32 vertices.
You have two options, which will both provide similar result here.


Edge > Bridge Edge loops 
Face > Fill, Alt+F




As @vklidu pointed out, Face > Fill gives different results in many cases, notably  when some faces are flipped.