7.6 (part 1), due March 23

The title of this section is "Normal Subgroups".  I thought these subgroups were kind of weird.  Does left congruent and left coset mean that you perform the group operation aka "multiply" on the left?  The theorems and properties of these subgroups entered my mind as the same properties of the other not normal subgroups we talked about earlier in the chapter.  I found myself wondering if these properties were the same or if there was a difference that I was somehow missing?