Could someone please explain me the concepts of the following terms? What do the different periods in time refer to and stand for? - Olam Hazeh (Acharit HaYamim) - Olam Haba - Yemot HaMashiach - Techiyat Hametim
Olam Hazeh refers to the state of the world we are currently in.
Acharit HaYamim and Yemot HaMashiach are synonymous, referring to the Messianic Age.
Techiyat HaMetim is the Resurrection of the Dead.
Olam Haba refers to the the last stage of existence after what would be 7000 AM.
There is some confusion as some sources switch names around when referring to the same thing. The ספר שפתי חיים חלק ב'פרק ב' of Rav Chaim Friedlander brings the כסף משנה as saying that the argument between the Ramba"m and the Raava"d regarding Olam Haba is really just that the Ramba"m calls Gan Eden (the temporary soul world according to your source) Olam Haba and the Raava"d calls Techiyat Hametim time Olam Haba, but they're actually referring to those two distinct times and not arguing about what Olam Haba is.
See the ספר שפתי חיים for a more comprehensive treatment of these subjects.