Node, Link, Node, Link, Node: Linking Nodes into a LinkedList
Methods &amp; Naming

You're building a collection so, implicitly, you're building a contract with your user that your class will act like a collection, that you'll stick to a protocol for collections objects.

If you wan't to grasp a little more on what I’m trying to say, you can read this article.

So, even though I agree with @Dair that size would be “saffer” as _size (but hey, we’re all responsible adults around here), I strongly disagree with the size property. You should implement it as a __len__ method and use it like:

stuff = LinkedList()
length = len(stuff)


Some other methods can have more common names too:


add \$-&gt;\$ apppend;
add_at \$-&gt;\$ insert or __setitem__:

__setitem__ will allow you to do stuff[3] = 'some value' and then insert is just a call to self[index] = value.

You will need to change the signature to def __setitem__(self, key, value).
remove \$-&gt;\$ pop (or maybe __delitem__); remove is prefered to remove by value instead of by index.
get \$-&gt;\$ __getitem__: it will allow you to do the_value = stuff[3]; you should also remove get_node as there is little to no interest in exposing your internals to the user.


Methods that are missing

You could implement an __iter__ method that will allow you to do:

stuff = LinkedList()
# populate stuff
for elem in stuff: # will use __iter__, or fail back to __len__ + __getitem__ if not available
    do_something(elem)


It will also help you shorten __getitem__. You can use something along the lines of:

def __iter__(self):
    node = self.first
    while node is not None: # No self.size involved, yay
        yield node.value
        node = node.after


You can also implement the __reversed__ iterator using the same logic (and use it in __getitem__ too.

Using a parameter to __init__ that default to None would also be usefull to build a LinkedList out of any iterable:

def __init__(self, other=None):
    self._size = 0
    self.first = None
    self.last = None

    if other is not None:
        for element in other:
            self.append(element)


It is then easy to create stuff = LinkedList([1,2,8,12]).

And finally, you should consider adding a __str__ or __repr__ method so you can print(stuff). Use __iter__ to simplify it.