(Scholars variously date the beginning of the "Middle Assyrian period" to either the fall of the Old Assyrian kingdom of Shamshi-Adad I, or to the ascension of Ashur-uballit I to the throne of Assyria.)
Ashur-uballit I
In the 15th century BC, Saushtatar, king of Hanilgalbat (Hurrians of Mitanni), sacked Ashur and made Assyria a vassal. Assyria paid tribute to Hanilgalbat until Mitanni power collapsed from Hittite pressure from the north-west and Assyrian pressure from the east, enabling Ashur-uballit I (1365 BC – 1330 BC) to again make Assyria an independent and conquering power at the expense of Babylonia; and a time came when the Kassite king in Babylon was glad to marry the daughter of Ashur-uballit, whose letters to Akhenaten of Egypt form part of the Amarna letters. This marriage led to disastrous results, as the Kassite faction at court murdered the Babylonian king and placed a pretender on the throne. Assur-uballit promptly marched into Babylonia and avenged his son-in-law, making Kurigalzu of the royal line king there.
Assyrian expansion
Hanilgalbat was finally conquered under Adad-nirari I, who described himself as a "Great-King" (Sharru rabû) in letters to the Hittite rulers. The successor of Adad-nirari I, Shalmaneser I (c. 1300 BC), threw off the pretense of Babylonian suzerainty, made Kalhu his capital, and continued expansion to the northwest, mainly at the expense of the Hittites, reaching Carchemish and beyond.
Shalmaneser's son and successor, Tukulti-Ninurta I, deposed Kadashman-Buriash of Babylon and ruled there himself as king for seven years, taking on the old title "King of Sumer and Akkad". Another weak period for Assyria followed when Babylon revolted against Tukulti-Ninurta, and later even made Assyria tributary during the reigns of the Babylonian kings Melishipak II and Marduk-apal-iddin I.
The correct chronology of these Assyrian kings is still is much debated. There are some crucial solar eclipse records. Wikipedia's Assyrian eclipse page refers to four such eclipses. For example, the Assyrian eclipse associated with June 15, 763 BC is widely accepted by the defenders of a middle chronology, but three ignored solar eclipses from the reign of Esarhaddon would affect the calculation drastically.
Tiglath-Pileser I reaches the Mediterranean Sea
As the Hittite empire collapsed from onslaught of the Phrygians (called Mushki in Assyrian annals), Babylon and Assyria began to vie for Amorite regions, formerly under firm Hittite control. When their forces encountered one another in this region, the Assyrian king Ashur-resh-ishi I met and defeated Nebuchadnezzar I of Babylon.
The son of Ashur-resh-ishi's, Tiglath-Pileser I, may be regarded as the founder of the first Assyrian empire. In 1120 BC, he crossed the Euphrates, capturing Carchemish, and defeated the Mushki and the remnants of the Hittites — even claiming to reach the Black Sea. He advanced to the Mediterranean, subjugating Phoenicia, where he hunted wild bulls. He also marched into Babylon twice, assuming the old title "King of Sumer and Akkad", although he was unable to depose the actual king in Babylonia, where the old Kassite dynasty had now succumbed to an Elamite one.
Society in the Middle Assyrian period
Assyria had difficulties with keeping the trade routes open. Unlike the situation in the Old Assyrian period, the Anatolian metal trade was effectively dominated by the Hittites and the Hurrians. These peoples now controlled the Mediterranean ports, while the Kassites controlled the river route south to the Persian Gulf.
The Middle Assyrian kingdom was well organized, and in the firm control of the king, who also functioned as the High Priest of Ashur, the state god. He had certain obligations to fulfill in the cult, and had to provide resources for the temples. The priesthood became a major power in Assyrian society. Conflicts with the priesthood are thought to have been behind the murder of king Tukulti-Ninurta I.
The main Assyrian cities of the middle period were Ashur, Kalhu (Nimrud) and Nineveh, all situated in the Tigris River valley. At the end of the Bronze Age, Nineveh was much smaller than Babylon, but still one of the world's major cities (population ca. 33,000). By the end of the Neo-Assyrian period, it had grown to a population of some 120,000, and was possibly the largest city of that time. All free male citizens were obliged to serve in the army for a time, a system which was called the ilku-service. The Assyrian law code, notable for its repressive attitude towards women in their society, was compiled during this period.