This is not an unusual request here at the Research Library. However, it is a surprisingly difficult one to answer. Yellowstone has been a national park for over a hundred years and has been in use for over 11,000 years and, either way you look at the question, that's a lot of ground to cover. Most people are really looking for a specific topic like the history of visitors to the park or the history of the automobile. But sometimes, we aren't able to get that information from our patron (if they write us an email or a letter), so we have to paint a broad picture and hope that some of the information that we give them will be useful. We can then wait to see if they give us more information. This particular patron also wanted some pictures of the Old Faithful Geyser. Here are portions of my reply:
Your inquiry was forwarded to us here at the Yellowstone Research Library. Thank you for your interest in the history of Yellowstone National Park. The park was established in 1872 when it was signed into law by President Ulysses S. Grant. There had been people in the area before. Native Americans have lived in the region for at least 11,000 years but the first official exploration was not until 1869. The US Army was called in to help enforce the law in 1886 and stayed until 1918. The National Park Service was created in 1916 and overlapped the Army for two years. The history since then has been very rich and includes such notable events as the 1959 Hebgen Lake Earthquake, the 1988 Fires, and the 1995 reintroduction of the Yellowstone wolves.
There are some really great books that talk about the history of Yellowstone and you should be able to get them through your local library. They include Aubrey Haines' "Yellowstone Story" and Richard Bartlett's "Yellowstone : A Wilderness Besieged." For books with some great pictures of the park, including geysers, check out "Geysers: When Earth Roars" by Roy A. Gallant, "Eye of the Grizzly" by Mike Graf, and "Discovering Yellowstone" by George B. Robinson.
There are also some online sources where you can do research. I'd start with the park's website is https://www.nps.gov. More information can also be found at http://greateryellowstonescience.org. There is an independent group of researchers that tracks geysers in the park and post their pictures and findings at http://www.geyserstudy.org.