The history book is not terribly long, and it's quite informative.
The history of magic in Sigmar's empire starts with Sigmar, founding his empire, and, when laying down his code of laws, forbidding witchcraft. Witchcraft was imprecisely defined (the book speculates that this is because it was based on dwarvern law, and there are no dwarf spellcasters), and thus, for a long time the law was inconsistently enforced, with many magic users (especially those with claims to divine power sources) going unprosecuted, or more often, erratically persecuted, and the forces of chaos having an ever-shifting morass of semi-legitimate cults, hedge witches, alchemists, court magicians, and majikers to hide themselves amongst. Many magical institutions existed in this period of time, but many of them fell to, or were revealed as tools of, the forces of chaos, and the rest hid themselves from persecution. The text disapproves strongly of this situation, clearly preferring either extreme to the ambiguity.
Then, Magnus the Pious decided, that, due to the great aid that elven spellcasters, especially the archmage Teclis (the text assumes you know who these people are) in defeating chaos, that the Empire should legalise magic in a controlled, careful way, in order to bring the human spellcasters who unambiguously existed into the fold. He asked Teclis to create a legal and magical framework and to teach it to the people of the empire. Teclis gathered the greatest human spellcasters of the era and founded the eight colleges of magic in Altdorf. Despite the extremely restrictive terms of the charter (the full text of which is provided), this was an extremely controversial decision only possible in the wake of Magnus's reunification of the Empire, his defeat of an Everchosen, his extreme levels of general popularity, and several cases of extremely conspicuous divine intervention.
So it continued until the reign of Dieter IV, one of the most despised Emperors on record. The night of a thousand arcane duels (when increasing tensions between the colleges resulted in them unleashing a storm of magic and erupting in outright warfare between the colleges, ending only when the Grand Theogenist of Sigmar stormed their towers and left no less than six of the eight college Patriarchs dead occurred early in his reign, and subject to pressure from the cult of Sigmar, he revoked the college's charter and outlawed magic, leading to a decades-long siege on the colleges, which never fell due to the truly terrifying danger that a building full of desperate archmages with no laws holding them back can pose. Dieter also sold a lesser charter to the elementalists of Nuln permitting them to practice magic in an attempt to make up for the lack, but they were for many reasons less effective. His final act of significance to this book was selling Marienburg its independence, which it has retained to this day, a decision which got not only him, but his dynasty dethroned.
His successor managed, with some difficulty, to have the colleges reinstated, but only after losing several wars to Marienburg due to its superior magical support (both in the form of the students of the newly founded college of sea magics, but also high elven mercenaries working alongside Marienburg, whose continued independence they favoured due to its prominence in maritime trade.)
The final chapter is a summary of the legal situation as it stands. In the Empire proper, users of arcane magic without a charter or similarly strong evidence in favour of their virtue are not permitted. Divine magic is permitted except from the worship of explicitly forbidden gods, of which there is an extensive list not attached. There is a substantial grey magic community nonetheless, the details of which the author was not aware of, but witch hunters and chartered wizards alike have a much stronger legal mandate to hunt them down and burn them or demand they join a college respectively. In Marienburg, there is a similarly long list of forbidden religions and magical practices, but unknown magical traditions come through with the foreign sailors often enough that it increases profitability to assume they are permissible unless there is any evidence to the contrary.