In Python, what is the difference between ".append()" and "+= []"?

In addition to the aspects described in the other answers, append and +[] have very different behaviors when you're trying to build a list of lists.

>>> list1=[[1,2],[3,4]]
>>> list2=[5,6]
>>> list3=list1+list2
>>> list3
[[1, 2], [3, 4], 5, 6]
>>> list1.append(list2)
>>> list1
[[1, 2], [3, 4], [5, 6]]

list1+['5','6'] adds '5' and '6' to the list1 as individual elements. list1.append(['5','6']) adds the list ['5','6'] to the list1 as a single element.