Alexander's empire did indeed dissolve shortly after his death. There are many reasons for this. One important reason was the lack of an heir. He had a young boy, Alexander IV, but he and his mother Roxanne were imprisoned in Amphipolis by Cassander. Cassander was one of Alexander's general and one of the most ambitious. Cassander would rule Macedonia after Alexander.

Alexander's empire would split into a few different parts immediately following his death. The large pieces were Macedonia, Egypt, Seleucia, and the Kingdom of Lysimachos (mostly Anatolia). What followed were known as the Diadochi Wars or the Successor Wars. These included dynasties founded by Alexander's generals including Ptolemy, Cassander, Lysimachos, and Seleucus. The next few decades were filled with war between the Hellenistic kingdoms. This period is known as the Hellenistic period and the Wars of the Diadochi.

We have sources available to us, but none of them are true primary sources. This means that there are none from the time of Alexander. Arrian, Plutarch, Diodorus, and Curtius have all written about Alexander. Some of them not far removed from the period in comparison. The argument against Alexander (there are many) usually stems from his kingship or lack thereof. Alexander was actually never asked to rule. He spent his entire reign in conquest and although he did show diplomatic skill, he never had to deal with real imperial problems.

If you are interested in the non-military Alexander and the empire(s) that followed, I suggest looking into these sources:

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Alexander's Empire by Gillman and Mahaffy

After Alexander: The Time of the Diadochi by Anson and Troncoso

Dividing the Spoils: The War for Alexander the Great's Empire by Robin Waterfield

Alexander's Heirs: The Age of the Successors by Edward Anson

Ghost on the Throne: The Death of Alexander the Great and the Bloody Fight for His Empire by James Romm

Alexander the Great Failure: The Collapse of the Macedonian Empire by John Grainger