Major events from 1820 to 1865.

There is some room for variation in this answer because I'm not sure whether the question is asking for major historical events within a certain country (like the United States) or if the answer can include world events. Additionally, there is some room for personal opinion to influence the answer. Some people are going to view certain events as more important and critical to that time period than other people.
As a general time period, those dates are during the Industrial Revolution. A lot of things happened during this time period, but in general it caused a shift from a rural, agrarian society to an urban, industrial society. Below I'll list some more specific events that occurred during that forty-five-year period:
1820: Maine becomes the twenty-third state.
1821: Napoleon dies.
1821: Missouri becomes the twenty-fourth state.
1823: The Monroe Doctrine instigated a United States policy that opposed European colonialism in the Americas.
1826 or 1827: The first photograph is taken by Joseph Nicéphore Niépce. The date is up for some interpretation.
1828: The Democratic Party is created.
1830: The Book of Mormon is published.
1836: The Battle of the Alamo. Also in this year, the Colt Revolver and John Deere Steel Plow are invented.
1844: Samuel Morse sends first electrical telegram.
1846–1848: The US and Mexican War.
1848: Gold is discovered in California and the Gold Rush is sparked.
1852: Uncle Tom's Cabin is published.
1860: Lincoln is elected President, and the Henry repeating rifle is invented.
1861–1865: The Civil War in the United States.
https://www.hrc.utexas.edu/exhibitions//