January 13 – American songwriter Stephen Foster ("Oh! Susanna", "Old Folks at Home") dies aged 37 in New York City, leaving a scrap of paper reading "Dear friends and gentle hearts". His parlor song "Beautiful Dreamer" is published in March.
January 16 – Denmark rejects an Austrian-Prussian ultimatum to repeal the Danish Constitution, which says that Schleswig-Holstein is part of Denmark.
January 21 – New Zealand Wars: The Tauranga campaign begins.
February – John Wisden publishes The Cricketer's Almanack for the year 1864 in England; it will go on to become the major annual cricket reference publication.
February 1 – Danish-Prussian War (Second Schleswig War): 57,000 Austrian and Prussian troops cross the Eider River into Denmark.
February 15 – Heineken Brewery is founded in the Netherlands.
February 17 – American Civil War: The tiny Confederate hand-propelled submarine H. L. Hunley sinks the , using a spar torpedo in Charleston Harbor, becoming the first submarine to sink an enemy ship, although the submarine and her crew of eight are also lost.
February 20 – American Civil War: The Union suffers one of its costliest defeats at the Battle of Olustee near Lake City, Florida.
February 25 – American Civil War: The first Northern prisoners arrive at the Confederate prison at Andersonville, Georgia (the 500 prisoners had left Richmond, Virginia, seven days before).
March 1 – Alejandro Mon y Menéndez takes office as Prime Minister of Spain.
March 9 – American Civil War: Abraham Lincoln appoints Ulysses S. Grant commander in chief of all Union armies.
March 10 – American Civil War: The Red River Campaign begins, as Union troops reach Alexandria, Louisiana.
March 11 – Great Sheffield Flood: A reservoir near Sheffield, England, bursts; 250 die.
April 8 – Gallaudet University is founded in Washington, D.C., as the first university for the deaf and hard of hearing.
April 12 – American Civil War: Battle of Fort Pillow – Confederate forces kill most of the African American soldiers that surrender at Fort Pillow, Tennessee.