Louisa May Alcott didn't really want to write a book for American girls. In fact, she claimed in her journal that she didn't even like girls, except her sisters. But once her publisher convinced her to try, she succeeded spectacularly and the public demanded sequels! (Source)
The first half of Little Women (through Chapter 23) is loosely based on Louisa May Alcott's memories of family life when she was a girl. Like Jo March, Louisa was a tomboy who wanted to be a writer. Also like Jo, Louisa had three sisters. (Source)
Unlike her heroine Jo March, Louisa May Alcott never married. Accordingly, the second half of Little Women is more fictional and less autobiographical than the first half. (Source)
After the publication of the first part of Little Women, readers would write to Louisa May Alcott and ask what happened to the girls and who they married. Many of them wanted Alcott to make Jo fall in love with Laurie. Alcott refused and wrote in her journal, "I won't marry Jo to Laurie to please anyone." In fact, she created the relationship with Professor Bhaer specifically because she thought it was "a funny match"! (Source)
Louisa May Alcott's father, Bronson Alcott, was a Transcendentalist philosopher and friend of Ralph Waldo Emerson. Bronson Alcott is best known for an unusual experiment in "utopian" communal living that he undertook at a farm called Fruitlands. Later in life, Louisa May Alcott wrote a satirical story describing Fruitlands titled "Transcendental Wild Oats" – a hilarious and short read, if you're interested! (Source)
Like Jo March, Louisa May Alcott made a living for a while writing sensational fiction and thrillers for the popular press. (Source)
There are two sequels to Little Women: Little Men and Jo's Boys, which tell the story of the boarding school that Jo and Professor Bhaer run at Plumfield.