In the beginning, there was only water and darkness. The ancient Egyptians understood the original water as a woman, Nun (or Naunet), and also called it Mut, for "mother." Ta-da!
Mut gets a huge temple of her own inside the giant, mile-long Karnak Temple complex. This is the first time we know Mut gets to wear the double crown. It's appropriate, since Hatshepsut is a female king (a woman who gets to wear the double crown herself).
Amunhotep III dedicates hundreds of life-sized stone statues of Sekhmet-Mut to the Mut temple at Karnak. They line the processional ways from the temple in all directions to scare off a plague that is killing many people in Egypt. Even today, many of these statues are still in place or featured in museum collections all over the world.
Under Akhenaten, Karnak and Luxor temples were closed, as he didn't like the priests of Amun-Ra. Mut's temples were also closed and her images were defaced. Boo.
One of the first things King Tut did, after Akhenaten died and he became king, was reopen the temples and start the worship of Egypt's many gods again. Mut's temples were restored alongside Amun-Ra's. One of the most beautiful statues in Karnak is an image of Tut and his wife Ankhesenamun sitting next to each other, dressed up as Amun-Ra and Mut. After King Tut died, his successor scratched out Tut's name and carved his own name and his wife's name on the statue (how rude). At least his wife's name, Mutnodjmet (meaning "Mut is sweet") was respectful.
Mut's temples continued to grow, probably because Ramses II and his first (and most beloved) wife Nefertari loved her so much. The feeling was mutual. How do we know? Nefertari's middle name was Merytmut, "the one Mut loves," and Ramses dedicated life-sized statues of his wife as Mut to Karnak, just like King Tut had done for his wife Ankhesenamun.
Mut, Isis, and Hathor are all different goddesses, with different backgrounds, husbands, and functions. Under the Ptolemaic pharaohs, though, they were put together to make a new super-goddess with the attributes of all three. At first, they kept all their names (as Isis-Mut-Hathor, or Hathor-Mut-Isis), but eventually, the three-form mother goddess that traveled to Rome and all the Roman Empire was just called Isis.
Rome's second emperor, Tiberius Caesar, rebuilt Mut's temple at Karnak after it was destroyed in a Nile flood. Eventually the Romans needed stone for other buildings, and so they started taking the place apart. We know these stones came from Mut's temple because they didn't bother to remove any of their original art or carvings.