About the Mesopotamian Astronomy
The history of astronomy in the world begins in Mesopotamia with the Sumerians who developed the earliest writing system-known as cuneiform-around 3500-3200 BC. In fact that many star names
Venus Tablet of King Ammizaduga
appear in Sumerian suggests a continuity reaching into the Early Bronze Age. Actually, our knowledge of Sumerian astronomy is indirect, via the earliest Babylonian star catalogues dating from about 1200 BCE. After Mesopotamian culture disappeared, only fragments of Babylonian astronomy have survived. Nevertheless, the surviving fragments show that, according to the historian A.Aaboe, Babylonian astronomy was "the first and highly successful attempt at gibing a refined mathematical description of astronomical phenomena"and that "all subsequent varieties of scientific astronomy, in the Hellenistic world, in India, in Islam, and in the West-if not indeed all subsequent endeavour in the exact sciences-depend upon Babylonian astronomy in decisive and fundamental ways."

Mesopotamian Calendar
Babylonian Calendar
The Acient Babylonian Calendar is the first twelve months calendar in the history. In the Babylonian Calendar, the year begins in Spring, ends in Winter, and there are three season in each year: reš šatti [it means beginning] , mišil šatti [it means middle] , and kīt šatti [it means end of the year]. In fact, the Babylonian Calendar is based on a calendar called Umma calendar of Shulgi.
Here is a video that tells you about Babylonian Calendar.

You can see Babylonian Calendar Here.
P.S.: I don't know who discovered the Babylonian Calendar, even I searched it on Google.
Detail of the Ishtar Gate in Babylon

Assyrian Calendar
Assyrian Calendar is based on Babylonian Calendar, but it's more digital than Babylonian Calendar. Assyrian astronomers created it in the year 4750 BC. It has 364 days, it's almost a solar year, and it has four season. Assyrian Calendar still begins in Spring, ends in Winter.

Mesopotamian Astrology
I don't think Astrology is very scientific, but it's really impotant to the Astronomy and History. Mesopotamian Astrology help us to know and understand their religion. There are 15 God and Goddesses in Mesopotamian History.They are Anshar, Anu (An), Apsu, Ea, Enlil, Ishtar (Inanna), Kishar, Marduk, Mummu (Mommu), Nintu (Ki),Shamash, Sin,Tiamat. If you want to see the details, please click Here.

About the knowledge of Solar System, Universe and the Earth
Sumerian know the Solar system, but actually lots of historian think that they only knew there are 10 planets around the Sun. Ea
Sumerian thought there are 10 planets around the Sun
ch planet represents a god/goddess. There are the series of cuneiform tablets called Enûma Anu Enlil. It recorded Venus's period motion.It's the earliest evidence that planet's were recognized as periodic. In fact the Mesopotamian Astronomers thought that the Earth are flat, surrounded by a huge, holed space, and on the sky, that's heaven. They also thought there are water in the universe and the side of earth.

Critical thinking
Mesopotamian astronomer improved the astronomy, they discovered many things, like solar system, planet's motion is periodic. Actually, many astronomy knowledge in the 21 century is based on Mesopotamian astronomy.

We learned a lot from them,even they just used their eyes to watched the sky and the stars, like Solar system. Also they have the 12 months calendar, just like us. But in some way, there are some differences between Mesopotamian and us, they thought that the Earth is flat, and there is heaven on the sky. Now, the astronomy are very scientific, we use high-tech telescope to watched the sky.

Before they started the history of astronomy, everyone don't know what's the date, what's the season, when can they plant crops, but now we know when can we plant crops, when can we gather crops, we have so many festival to celebrate, and they are all based on the different 12-months calendars.

Astronomy of Mesopotamia: http://www.thelivingmoon.com/43ancients/01documents/Mesopotamian_Astronomy.html
Detail of the Ishtar Gate in Babylon: http://upload.wikimedia.org/wikipedia/commons/0/0e/Babylon_relief.jpg
Did the ancient Sumerian know about our "Solar system": http://www.edwardtbabinski.us/geocentrism/sumerians.html
The Lunar/Solar Calendar from Mesopotamia: http://www.youtube.com/embed/-SuUE7epAXg
Wikipedia, Assyrian Calendar: http://en.wikipedia.org/wiki/Assyrian_calendar
Wikipedia, Babylonian Astronomy: http://en.wikipedia.org/wiki/Babylonian_astronomy
Wikipedia, Babylonian astrology: http://en.wikipedia.org/wiki/Babylonian_astrology
Wikipedia, Babylonian Calendar: http://en.wikipedia.org/wiki/Babylonian_calendar
Wikipedia, History of Astronomy [Mesopotamia]: http://en.wikipedia.org/wiki/History_of_astronomy#Mesopotamia
Wikipedia, Mesopotamia: http://en.wikipedia.org/wiki/Mesopotamia

By Ingrid