Beneath that blanket of sediment, the Lower Peninsula is a geologic basin, the Michigan Basin, that has been occupied by shallow seas for most of the last 500 million years as it slowly warped downward under the weight of its sediments. The central part filled in last, its shale and limestone dating from the Late Jurassic Period around 155 million years ago. Its outer rim exposes successively older rocks going back to the Cambrian (540 million years ago) and beyond on the Upper Peninsula.
The rest of the Upper Peninsula is a cratonic upland of very ancient rocks from as long ago as Archean times, nearly 3 billion years ago. These rocks include the iron formations that have supported the American steel industry for many decades and continue to be the nation's second-largest producer of iron ore. See a gallery of Michigan geological attractions.
I have prepared two other versions of the Michigan geologic map. The first version (2000x2400 pixels, 360 KB) has each named formation shown along with a key. The other, more aesthetically pleasing, is a scan of the state's 1968 map showing the rock units denoted by time instead of name, and it also includes the surrounding geography and avoids the floating-in-space effect. That's here in a 1200x1550 pixel version (840 KB)and a 2100x2700 pixel version (2 MB), because I can't bear to waste a good scan.