Well, katrielalex is right about itertools, but the OP seems to be rather more interested (or should be!) in learning to manipulate the basics of the built-in data structures. As for manipulating a list in place, it does need thought, but my recommendation would be to read through this section of the documentation and try a few list methods (hint: list.pop(), list.remove(), and learn everything about slices.)
The posted code could be simplified, by the way (you should however add handling of error conditions):
def remove_adjacent(nums):
a = nums[:1]
for item in nums[1:]:
if item != a[-1]:
a.append(item)
return a
