The Michigan/Notre Dame rivalry began as a teaching tool per ESPN's recent article of "Strange but True Historical Facts for Each Top 25 Team" from earlier today.
Per Harry Lyles Jr., Michigan is responsible for teaching the Irish how to play football, which dates all the way back to 1884.
One of Michigan's biggest rivals to this day is Notre Dame, and the Wolverines have themselves to thank for it, at least in a way. In 1884, Notre Dame sent Michigan a letter requesting Michigan to teach its students how to play football.
In 1887, it finally happened and Michigan won 8-0. In the Scholastic, the Notre Dame student magazine, an article mentioned the following:
On account of time, only a part of one inning was played, and resulted in a score of 8 to 0 in favor of the visitors. The game was interesting, and, notwithstanding the slippery condition of the ground, the Ann Arbor boys gave a fine exhibition of skilful playing. This occasion has started an enthusiastic football boom, and it is hoped that coming years will witness a series of these contests.
There would indeed be a series of future contests.
The Wolverines and Irish would go on to play 43 times over the next 100-plus years with U-M edging out the other Midwestern, traditional powerhouse.
Michigan currently leads the series 25-17-1 and will have the last laugh for the foreseeable future after pounding the Golden Domers 45-14 in Ann Arbor this past season. Michigan also has the largest margin of victory at 38-0 from the 2003 matchup and the longest win streak of eight games, which started when the rivalry began all the way back in 1887.