Ich werde mir das anschauen
The translation is given as "I will look at that." What function does the "mir" serve? It seems redundant with the "Ich".
Some verbs are reflexive verbs and just require that reflexive pronoun. So here the basic verb is "sich (dat) etwas (ack) anschauen". The same verb can also mean to look at oneself, in which case it's "sich (ack) anschauen". Other verbs exist both as reflexive and non-reflexive, with different meanings.
I'm not sure how thorough the tips and notes are for this in the German course, but try googling "reflexive verbs German", and it should all become clear! :-)
It's a bit like "I will look at it for my benefit", I think.
It's similar to the dative-of-benefit in sentences such as Ich habe meiner Mutter ein Buch gekauft "I bought my mother a book", which says not only that you bought a book but that the result of the buying somehow benefited your mother.
So here, the looking benefits you.
I find it a bit difficult to explain in English what the different "feeling" is between Ich werde das ansehen and Ich werde mir das ansehen -- the second is perhaps "I will look at it so that I can form an opinion of it".
- Ich schaue den Baum an. (etwas anschauen)
- Ich schaue mir den Baum an. (sich etwas anschauen)
Both are valid sentences, but the meaning is different.
The first one only means you are looking at it, with no deeper intention.
The second one implies you are somehow interested in the tree, recognising the details. It could also mean you are inspecting the tree.